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Cluster counting in drift chambers for particle identification and tracking Caron, Jean-François 2015

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Cluster Counting in Drift Chambers for ParticleIdentification and TrackingbyJean-Franc¸ois CaronB.Sc. Hon. Physics, University of Calgary, 2006M.Sc., The University of British Columbia, Vancouver, 2009a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoralstudies(Physics)The University of British Columbia(Vancouver)December 2015c© Jean-Franc¸ois Caron, 2015AbstractDrift chambers are a type of gaseous ionization detector used in high-energyphysics experiments. They can identify charged particles and measure theirmomentum. When a high-energy charged particle crosses the drift chamber,it ionizes the gas. The liberated electrons drift towards positive-high-voltagewires where an ionization avalanche amplifies the signal. Traditional driftchambers use only the arrival time of the cluster of charge from the closestionization for tracking, and use only the integral of the whole signal forparticle identification.We constructed prototype drift chambers with the ability to resolve thecharge cluster signals from individual ionization events. Different algorithmswere studied and optimized to best detect the clusters. The improvementsto particle identification were studied using a single-cell prototype detector,while the improvements to particle tracking were studied using a multiple-layer prototype. The prototypes were built in the context of initial workfor the now-cancelled SuperB project, but the results apply to any driftchambers used in flavour-factory experiments.The results show that the choice of algorithm is not as critical as properlyoptimizing the algorithm parameters for the dataset. We find that a smooth-ing time of a few nanoseconds is optimal. This corresponds to bandwidth ofa few hundred megahertz, indicating that gigahertz-bandwidth electronicsare not required to make use of this technique.Particle identification performance is quantified by the fraction of real pi-ons correctly identified as pions with at most 10% of real pions mis-identifiedas muons. In our single-cell prototype, the performance increases from 50%iito 60% of pions correctly identified when cluster counting is combined witha traditional truncated-mean charge measurement, compared to the chargemeasurement alone.Tracking performance is quantified by the single-cell resolution: the un-certainty in measuring the distance of charged particle tracks from a givensense wire. In our multiple-layer prototype, the single-cell tracking resolu-tion using traditional methods is measured to be ∼ 150µm. With clustercounting implemented, the resolution is unchanged, indicating that the ad-ditional cluster information is not useful.iiiPrefaceThe first half of my research project was a study of the single-cell pro-totype particle tracking detectors which we call the TRIUMF prototypes.They are described in Section 4.2 and were built at TRIUMF by Philip Lu,Rocky So, and Wayne Faszer; the amplifiers used were designed and con-structed by Jean-Pierre Martin at the Universite´ de Montre´al. A beam testwas performed with the help of fellow SuperB collaboration members andTRIUMF staff: Christopher Hearty, Philip Lu, Rocky So, Racha Cheaib,Jean-Pierre Martin, Wayne Faszer, Alexandre Beaulieu, Samuel de Jong,Michael Roney, Riccardo de Sangro, Giulietto Felici, Giuseppe Finocchiaro,Marcello Piccolo, Wyatt Gronnemose, and Steven Robertson.With the data from the beam test, I performed a particle-identificationstudy and the results were published in the paper titled “Improved particleidentification using cluster counting in a full-length drift chamber proto-type”, published by Elsevier in the journal Nuclear Instruments and Meth-ods in Physics Research Section A: Accelerators, Spectrometers, Detectorsand Associated Equipment, Volume 735, on January 21 2014, Pages 169-183 [1]. The article was written by me, except for the section describingthe amplifiers which was written by Jean-Pierre Martin. The coding andanalysis in the paper was entirely done by me, with consultation from theabove-mentioned people in the SuperB collaboration. The content of thatarticle is included in Chapter 4, with permission from the publisher and co-authors. Jerry Va’vra lent us the MCPs for our TOF system, and HirohisaTanaka lent us the oscilloscope for our data acquisition. In addition to theauthors of the resulting article, Wyatt Gronnemose and Steven Robertsonivassisted during the beam test.The second half of my research project involved the multi-cell prototypecalled “proto 2” or the Italian prototype, and is described in Chapter 7. TheItalian prototype was constructed at the Laboratorio Nazionale di Frascatiby myself and Riccardo de Sangro, Giulietto Felici, Giuseppe Finocchiaro,and Marcello Piccolo. The beam test was performed at TRIUMF by thesame people from the TRIUMF prototype beam test. The coding and anal-ysis for tracking was done entirely by me in consultation with ChristopherHearty.Several contributions were made to open-source programs. The mostnotable is the addition of a new interpolation method to the GNU ScientificLibrary [2]. Many bug reports and some patches were submitted to thedevelopers of ROOT [3] and Garfield [4]. The largest patch involved cor-rections to gender-specific pronouns used in documentation; it is describedin Appendix A.4. The analyses in this work also made extensive use ofthese open-source programs: Python [5], IPython [6], PyROOT [7] andNumPy [8].This work was supported by the Natural Sciences and Engineering Re-search Council of Canada and TRIUMF.My supervisory committee members were Christopher Hearty, Janis McKenna,Joanna Karczmarek, and Kris Sigurdson. Sherry Leung assisted with edit-ing and proofreading. Figures 1.3, 1.4, 7.4, 7.9, and 7.18 were made by AlonHershenhorn.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Flavour Physics . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Drift Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.1 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.2 Particle Identification . . . . . . . . . . . . . . . . . . 112 Design Considerations of Drift Chambers . . . . . . . . . . 172.1 Overall Design . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Gas Composition . . . . . . . . . . . . . . . . . . . . . . . . . 202.3 Wire Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4 Outer Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 252.5 Ageing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27vi3 SuperB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2 SuperB Drift Chamber . . . . . . . . . . . . . . . . . . . . . . 334 Particle Identification Study . . . . . . . . . . . . . . . . . . 404.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.1.1 Drift Chambers . . . . . . . . . . . . . . . . . . . . . . 414.1.2 Cluster Counting . . . . . . . . . . . . . . . . . . . . . 424.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2.1 Prototype Drift Chambers . . . . . . . . . . . . . . . . 454.2.2 Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.3 Wire Voltages . . . . . . . . . . . . . . . . . . . . . . . 494.2.4 Cabling . . . . . . . . . . . . . . . . . . . . . . . . . . 504.2.5 Test Beam . . . . . . . . . . . . . . . . . . . . . . . . 514.2.6 Time of Flight . . . . . . . . . . . . . . . . . . . . . . 524.2.7 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 544.2.8 Data Acquisition System . . . . . . . . . . . . . . . . 554.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.4 Beam Test Data . . . . . . . . . . . . . . . . . . . . . . . . . 574.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.5.1 Single-Cell Information . . . . . . . . . . . . . . . . . 594.5.2 Track Composition . . . . . . . . . . . . . . . . . . . . 644.5.3 Combined Likelihood Ratio . . . . . . . . . . . . . . . 674.5.4 Figures of Merit . . . . . . . . . . . . . . . . . . . . . 704.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.6.1 Charge Integration . . . . . . . . . . . . . . . . . . . . 714.6.2 Cluster Counting . . . . . . . . . . . . . . . . . . . . . 724.6.3 Cluster Timing for PID . . . . . . . . . . . . . . . . . 764.6.4 Dependence of PID on Gas Gain . . . . . . . . . . . . 774.6.5 Momentum . . . . . . . . . . . . . . . . . . . . . . . . 784.6.6 Dependence of PID on Window (Z-position) . . . . . . 784.6.7 Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.6.8 Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . 82vii4.6.9 Summary of Results . . . . . . . . . . . . . . . . . . . 824.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.8 Cluster-Counting Algorithms . . . . . . . . . . . . . . . . . . 854.8.1 Smoothing Procedures . . . . . . . . . . . . . . . . . . 854.8.2 Signal above Average . . . . . . . . . . . . . . . . . . 864.8.3 Smooth and Delay . . . . . . . . . . . . . . . . . . . . 874.8.4 Second Derivative . . . . . . . . . . . . . . . . . . . . 874.8.5 Timeout Booster . . . . . . . . . . . . . . . . . . . . . 885 Multi-Cell Prototype . . . . . . . . . . . . . . . . . . . . . . . 905.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.2 Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.4 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966 Theoretical Tracking Improvements . . . . . . . . . . . . . . 1026.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.2 Distances Along the Track . . . . . . . . . . . . . . . . . . . . 1056.3 Distances From the Wire . . . . . . . . . . . . . . . . . . . . 1076.4 Bayesian Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 1116.4.1 The First Cluster . . . . . . . . . . . . . . . . . . . . . 1126.5 The Second Cluster . . . . . . . . . . . . . . . . . . . . . . . . 1146.6 More Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1177 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.2 Measuring the Arrival Times . . . . . . . . . . . . . . . . . . 1207.3 Garfield Time-to-Distance Relations . . . . . . . . . . . . . . 1247.3.1 Interpolation . . . . . . . . . . . . . . . . . . . . . . . 1277.4 Track Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297.4.1 Track Initial Parameters . . . . . . . . . . . . . . . . . 1327.4.2 Minimization Troubles . . . . . . . . . . . . . . . . . . 1337.4.3 Track Parameter Uncertainties . . . . . . . . . . . . . 135viii7.5 Iterative Refinement and Resolution Measurement . . . . . . 1407.6 Timing Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . 1457.6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . 1457.6.2 Overview of Technique . . . . . . . . . . . . . . . . . . 1467.6.3 Algorithms and Parameters . . . . . . . . . . . . . . . 1497.7 Combined Likelihood . . . . . . . . . . . . . . . . . . . . . . . 1537.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1578 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1608.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . 1608.1.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . 1608.1.2 Particle Identification . . . . . . . . . . . . . . . . . . 1618.1.3 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 1628.2 Future Improvements . . . . . . . . . . . . . . . . . . . . . . . 1638.2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . 1638.2.2 Particle Identification . . . . . . . . . . . . . . . . . . 1648.2.3 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 1658.2.4 Other Ideas . . . . . . . . . . . . . . . . . . . . . . . . 167Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169A Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . 180A.1 The Novosibirsk Function . . . . . . . . . . . . . . . . . . . . 180A.2 Track Distance From a Wire . . . . . . . . . . . . . . . . . . . 182A.3 Cluster Time Likelihood Calculation . . . . . . . . . . . . . . 184A.4 Superfluous Gendered Language in Open-Source Project Doc-umentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185A.5 Combining Bessel and Struve Functions . . . . . . . . . . . . 187A.6 Personal Philosophy of Science . . . . . . . . . . . . . . . . . 188A.6.1 Science . . . . . . . . . . . . . . . . . . . . . . . . . . 188A.6.2 Physical Science . . . . . . . . . . . . . . . . . . . . . 190ixList of TablesTable 2.1 Wire materials used in the drift chambers of various his-torical experiments. . . . . . . . . . . . . . . . . . . . . . . 24Table 4.1 Summary of optimal parameters for cluster-counting algo-rithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75xList of FiguresFigure 1.1 Illustration of the ionization, drift, and avalanche process. 7Figure 1.2 Continued illustration of ionization, drift, and avalanche. 8Figure 1.3 Illustration of the charge division technique. . . . . . . . . 11Figure 1.4 Illustration of the time delay technique. . . . . . . . . . . 12Figure 1.5 Plot of a Landau distribution. . . . . . . . . . . . . . . . . 14Figure 2.1 Schematic of a planar chamber layout. . . . . . . . . . . . 18Figure 2.2 Schematic of the OPAL Central Jet Chamber. . . . . . . 19Figure 2.3 Cylindrical chamber layout for the ARGUS drift chamber. 20Figure 2.4 Photo of the BaBar drift chamber during construction. . . 26Figure 2.5 Example of two endplate designs considered for SuperB. . 26Figure 3.1 SuperB drift chamber schematic. . . . . . . . . . . . . . . 36Figure 4.1 Annotated photo of PID beam test setup. . . . . . . . . . 46Figure 4.2 Garfield simulation of electron drift isochrones. . . . . . . 47Figure 4.3 Circuit diagram of high-voltage connections. . . . . . . . . 48Figure 4.4 Schematic of amplifiers. . . . . . . . . . . . . . . . . . . . 50Figure 4.5 Schematic of beam test setup. . . . . . . . . . . . . . . . . 51Figure 4.6 Time-of-flight histograms. . . . . . . . . . . . . . . . . . . 53Figure 4.7 Example drift chamber signals. . . . . . . . . . . . . . . . 55Figure 4.8 Garfield simulation of energy lost by charged particles. . . 57Figure 4.9 Garfield simulation of charge clusters. . . . . . . . . . . . 58Figure 4.10 Histogram of charge integration start times. . . . . . . . . 61Figure 4.11 Sample event in chamber A showing 600 ns integration time. 62xiFigure 4.12 Integrated charge distributions for particles and asyn-chronous triggers. . . . . . . . . . . . . . . . . . . . . . . 63Figure 4.13 Integrated charge distributions by particle type. . . . . . 64Figure 4.14 Illustration of two smoothing algorithms. . . . . . . . . . 65Figure 4.15 Illustration of cluster-counting algorithms. . . . . . . . . . 66Figure 4.16 Distribution of cluster counts by particle type. . . . . . . 67Figure 4.17 Distribution of truncated mean of charges in a track. . . . 68Figure 4.18 Distribution of clusters per cm in a track. . . . . . . . . . 69Figure 4.19 PID efficiency graph comparing all techniques. . . . . . . 70Figure 4.20 PID efficiency as a function of charge integration time. . . 72Figure 4.21 Performance “heat map” used to optimize an algorithm. . 73Figure 4.22 Distribution of cluster time intervals, by particle type. . . 76Figure 4.23 PID performance with different gas gains. . . . . . . . . . 78Figure 4.24 PID performance with different momenta. . . . . . . . . . 79Figure 4.25 PID performance at different windows. . . . . . . . . . . . 80Figure 4.26 PID performance with different cable types. . . . . . . . . 81Figure 4.27 PID performance with different amplifiers. . . . . . . . . . 83Figure 5.1 Layout of all the wires in proto 2. . . . . . . . . . . . . . 92Figure 5.2 Microscope image of wires. . . . . . . . . . . . . . . . . . 93Figure 5.3 Schematic of feedthrough and tensioning. . . . . . . . . . 95Figure 5.4 Structural frame and wires of proto 2. . . . . . . . . . . . 96Figure 5.5 Photo of outer shell of proto 2. . . . . . . . . . . . . . . . 97Figure 5.6 Photo of window repair on proto 2. . . . . . . . . . . . . . 98Figure 5.7 Proto 2 high-voltage circuit. . . . . . . . . . . . . . . . . . 99Figure 5.8 Photo of instrumented end of proto 2. . . . . . . . . . . . 100Figure 5.9 Proto 2 mounted for beam test at LNF. . . . . . . . . . . 101Figure 6.1 Illustration of model. . . . . . . . . . . . . . . . . . . . . . 104Figure 6.2 Probability distributions of ionization event distances alongthe track. . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Figure 6.3 Probability distributions of ionization event distances fromthe wire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109xiiFigure 6.4 Probability distributions of second ionization event dis-tances from the wire. . . . . . . . . . . . . . . . . . . . . . 110Figure 6.5 Probability distribution of impact parameter with 1 cluster.114Figure 6.6 Probability distribution of impact parameter with 2 clusters.116Figure 6.7 Probability distribution of impact parameter with 3 clusters.118Figure 7.1 Example signal from a cell in proto 2. . . . . . . . . . . . 122Figure 7.2 Arrival time distribution for signals in proto 2. . . . . . . 123Figure 7.3 Derivative of arrival time distribution for signals in proto 2.124Figure 7.4 Illustration of point and distance of closest approach. . . 125Figure 7.5 Example of Novosibirsk fits to Garfield data. . . . . . . . 127Figure 7.6 Simulated resolution and distance-to-time relation. . . . . 128Figure 7.7 Comparison of interpolation methods. . . . . . . . . . . . 130Figure 7.8 Tangent circles for tracking. . . . . . . . . . . . . . . . . . 131Figure 7.9 Diagram showing track parameters. . . . . . . . . . . . . 132Figure 7.10 Schematic of x0 calculation for vertical tracks. . . . . . . 134Figure 7.11 Schematic of x0 calculation for non-vertical tracks. . . . . 135Figure 7.12 Function to be minimized for tracking. . . . . . . . . . . . 136Figure 7.13 Rainbow colour scheme for heat maps. . . . . . . . . . . . 137Figure 7.14 Illustration of two potential track candidates. . . . . . . . 138Figure 7.15 Example plots of tracking residuals. . . . . . . . . . . . . 141Figure 7.16 Resolution, time-to-distance relation, and corrections. . . 143Figure 7.17 Distribution of track distances. . . . . . . . . . . . . . . . 144Figure 7.18 Two signals with the same arrival time. . . . . . . . . . . 147Figure 7.19 Example empirical distribution functions for cluster ar-rival times. . . . . . . . . . . . . . . . . . . . . . . . . . . 148Figure 7.20 Comparison of cluster time distributions at two thresholds.150Figure 7.21 Residuals from Monte Carlo cluster time likelihoods. . . . 151Figure 7.22 Algorithm threshold optimization. . . . . . . . . . . . . . 152Figure 7.23 Clusters found on signal trace. . . . . . . . . . . . . . . . 154Figure 7.24 Negative log likelihoods. . . . . . . . . . . . . . . . . . . . 155Figure 7.25 Cluster time distributions at four distances. . . . . . . . . 156Figure 7.26 Tracking residuals with cluster counting. . . . . . . . . . . 158xiiiFigure 7.27 Single-cell resolution comparison. . . . . . . . . . . . . . . 159Figure A.1 Novosibirsk function. . . . . . . . . . . . . . . . . . . . . . 181xivAcknowledgementsI would like to thank all my physics teachers and instructors over the years.Each of you have contributed piece-by-piece to my overall understanding ofthe physical world, and hopefully you continue to inspire others.I want to thank my partner Sherry Leung for tremendous emotionalsupport, and my family for setting me up to succeed in my endeavours.While personal achievement is partially based on individual achievement,I must acknowledge that part of it is based on privilege. My work on thisproject was greatly assisted by my being born in Canada as a white cis-gendered male, heterosexual, into a middle-class family, and other categories.I did not choose to have this privilege, but I benefit from it regardless, andI am glad to be using it for something I believe is good.xvChapter 1Introduction1.1 Particle PhysicsParticle physics is the study of the smallest and most-indivisible constituentsof the physical world. What are currently called atomic physics and nuclearphysics used to be seen the same way that particle physics is seen now. As welearned more about the constituents of the objects of study (atoms, nuclei),these fields revealed even more elementary objects. As far as we know, theelementary particles of particle physics cannot be divided or reduced anyfurther.In a sense, current high-energy particle physics is the limit of reductionistscience. Reductionism is an approach where a complex system is investigatedby breaking it down into smaller independent components. One can see asteady progression of this approach from early chemistry to atomic physics,nuclear physics, and now particle physics.The terms “elementary” and “fundamental” are often added to particlephysics to mean explicitly those particles that are indivisible even at thehighest energies imaginable. There are still-divisible entities that are per-fectly well-described at certain energies by particle models, such as protons.Though the terms are interchangeable, I prefer the term “elementary” be-cause it has more reductionist implications - they are the simplest systemsavailable for study.1In order to access the energy scales and sizes relevant to particle physics,enormous energies are required. Studying these interactions is a fruitfulpart of astrophysics, as these energies are routinely present in cosmic rayinteractions in the upper atmosphere. Unfortunately cosmic ray collisionsare not controlled enough and do not have the high rates required to studythe rare and exotic interactions and species in particle physics. The ongoingsuccess of particle physics experiments has resulted in the latest projectsbeing some of the largest, most complex, and most powerful machines inthe world.1.2 Flavour PhysicsFlavour physics is a branch of particle physics concerned with the trans-formation of quarks and neutrinos (elementary particles) into other kindsof quarks and neutrinos. It could be described romantically as a modernalchemy. Probably the most interesting result of flavour physics research isthe discovery of quark mixing and CP violation. A good popular explanationof these phenomena can be found in the Fall 2006 issue of the physics@mitonline newsletter [9].Quark mixing is a phenomenon in which a given type of quark (up, down,strange, charm, top, bottom) is observed to spontaneously transform intoanother type. The explanation relies on the idea of two different “views”of quarks. In the “interaction” view, the relevant quarks are the ones weusually see in tables of the elementary particles. Quarks produced in inter-actions (including when we observe them) use this view. The other view isthe “propagation” view, and in this view the relevant quarks are mixtures(quantum superpositions) of the quarks in the interaction view. The prop-agation view is used when quarks are moving through space and time. Thepropagation quark states are not given clever names, and since they havea majority component that is one of the interaction quarks, we typicallyjust use the majority component’s name with a prime (′). The mixture issymmetric, so one could think of an up quark as a mixture of up′, charm′and top′ states, or one could think of an up′ as a mixture of up, charm, and2top quarks.When a particle with a given set of quarks is created in an interaction,it is in a “pure” interaction state: its quarks are unambiguously up, down,or whatever. When a given particle is measured, e.g., detected in a particledetector, it is also unambiguously in a pure interaction state. However sincethere is always a time lag between these two events, the particle that wedetect might not be the same kind as the one that was originally created.Along the way, some of the quarks might have transformed. The types ofparticles that can be observed are not ridiculous: energy, charge, and otherphysical quantities have to be conserved, but nevertheless this is an unusualprocess. No other known physics can change the identity of a particle simplyby having it travel through space.The most interesting consequence of quark mixing is CP symmetry vio-lation. CP stands for “charge and parity” and represents a total inversionof charge and the spatial coordinate system. If you have a spin-up electronmoving to the left and apply the CP operation, you now have a spin-downpositron moving to the right. For a long time it was believed that the lawsof particle physics were invariant under the CP transformation, i.e., that CPwas a symmetry of nature. The strong and electromagnetic interactions doexhibit CP symmetry (as far as we know), but the weak interaction does not.The weak interaction is the one responsible for the quark mixing explainedabove.A particular result of CP symmetry violation is found in the decay of neu-tral kaons. There are two states in which you can find a neutral kaon, calledK0 and K¯0, with different quark compositions (ds¯ and sd¯ respectively). Be-cause of quark mixing, a K0 can transform into a K¯0 and vice-versa, andkaons produced in experiments are quantum superpositions of these states.Neutral kaons predominantly decay via the weak interaction, but there aretwo kinds of decays: one with a short lifetime (∼ 10−9 s) resulting in twopions and one with a long lifetime (∼ 10−8 s) resulting in three pions. In anexperiment where you let the short-lived components of neutral kaons decayaway, there are still anomalous “long-lived” decays of the remaining neutralkaons to two pions. This would not be possible if the weak interaction did3not violate the CP symmetry. This is exactly the mechanism by which CPviolation was discovered in 1964 [10], leading to a Nobel Prize being awardedto Cronin and Fitch in 1980.An intuitive explanation (i.e., oversimplification) of CP violation is thatthere is a difference between matter and anti-matter, or equivalently, thatphysical processes that involve the weak interaction are fundamentally dif-ferent going forwards or backwards in time. This description relies on theCPT theorem which is quite important for quantum field theory, but insome exotic theories (e.g., non-local theories, or those that break Lorentzinvariance) there is no equivalence between CP violation and time-reversal.1.3 Drift ChambersIn order to perform experiments in particle physics, we need devices that candetect the particles and measure their properties. There are a wide varietyof such devices that detect different kinds of particles or measure differentthings, so a typical large particle physics experiment will employ many dif-ferent types of detectors in order to fully characterize the physical processesthat are happening. Drift chambers are one such kind of device [11].Drift chambers consist of a volume of gas with thin metal wires strungthroughout. When a high-energy charged particle crosses the gas (in ∼0.5 ns), it has a chance of interacting with the gas atoms or molecules. Ifthe interaction frees electrons from the gas atoms, this is called ionization.The charged atoms that are left behind after freeing the electrons are calledions. Metal wires are held at high and low voltages by external electronics,creating an electric field to which the electrons and ions will react.Drift chambers only detect charged particles; neutral particles are invis-ible to a drift chamber. They can determine the trajectory that a chargedparticle took when it passed through the detector. We call the trajectory the“track”. If the drift chamber is in a magnetic field, its measurement of thetrack can be used to determine the particle’s momentum. Drift chamberscan also reasonably distinguish between different kinds of charged particles.For example they can tell the difference between electrons, pions, and kaons,4even if these all have the same momenta. “Reasonably” here means that theidentification is sometimes ambiguous, and generally other types of detectorswill be used to more confidently identify particles. An advantage of driftchambers is that their signals are very fast to obtain, thus the drift chamberin a big experiment is often used as part of a “trigger”. The trigger is asignal to the whole experimental system that an interesting particle collisionor event has happened, and thus to record the data from that interaction.Most well-understood but uninteresting events (called background events)are not recorded, saving considerable computer resources.The negatively charged electrons will drift towards the high voltage wires(hence the name drift chambers), and the positively charged ions will drifttowards the low voltage wires. The ions are much heavier, so they takemuch longer to drift all the way to the wire (∼ 100 ns for electrons, ∼ 1µsfor ions). For most of the volume of the gas, the electrons drift at a constantspeed, with the electrostatic attraction to the wires balanced by collisionswith the gas. These collisions slightly change the direction in a random way.The average trajectory of the drifting electrons still goes towards the wire,but the side-to-side deviations from this path can affect the eventual timingmeasurement that will be made. This effect is diffusion. While the electronshave a constant drift speed, the electrons are slow enough that the collisionswith the gas do not ionize it. This changes when the electrons get very closeto the wires.The high-voltage wires are very thin (∼ 25µm is typical), while the low-voltage wires are typically thicker (∼ 100µm). Very thin wires can havehuge electric fields near their surfaces because the electric field varies asV/r, with the minimum r being the radius of the wires. The electric field isso large near the surface (e.g., within a few µm) that the drifting electronsaccelerate to high enough speeds to ionize more gas particles and liberatemore electrons. These new electrons are also accelerated by the electric field,ionize more gas, and so on. Eventually the cluster of electrons is collectedon the wire and the process finishes. This self-amplifying process is calledan avalanche and is one of the critical processes in the operation of driftchambers. The ions do not form avalanches because the low-voltage wires5are much thicker and the ions are much heavier, so the electric fields donot accelerate the ions enough to further ionize the gas. This is intentional,because the avalanches create huge numbers of electron-ion pairs. An ionavalanche at a low-voltage wire would create lots of electrons that wouldeventually drift back to the high-voltage wire and create yet-more electrons,and vice versa.The large number of electrons and ions created by the avalanche processcan be thought of as two clusters of moving charge - one negatively chargedand one positively charged (see Figures 1.1 and 1.2 for an illustration).These moving charges near the sense wire induce a current, which is pickedup by the electronics at the end(s) of the wires. There, amplifiers will furtherincrease the amplitude of the signal before sending it to a digitizer and finallyinto some processing systems so that the signal can be used. The electronsfrom the avalanche only move ∼ 1µm before hitting the sense wire, whilethe ions must drift across the whole cell. This means that the majority ofthe induced signal is actually produced by the ion’s movement [12]. Thelargest current is induced immediately when the charges are moving fast inthe strong electric field near the sense wire (∼ ns), but the ions drift for∼ µs before finally reaching the field wires on the edge of the cells. Thus therecorded signal has a sharp spike at the beginning followed by a long tail.Each ionization event from the original high-energy charged particle pro-duces a separate cluster, but almost always multiple avalanches will hit thesame wire. The signal is recorded as a series of voltage measurements atregular time intervals, and the individual clusters would look like spikeswith a sharp leading edge and a slower decay (e.g., Figure 7.18). The timeat which the first spike is seen in the signal is called the arrival time. Thenumber of spikes gives the number of original ionizations that resulted in acluster hitting the wire. The integral of the entire signal yields a quantityproportional to how many electrons hit the wire in total.6·◦◦◦◦◦SenseWirePOCAµ+????(a) Charged particle track, primaryionizations and delta-ray (t ∼ ns).·◦◦◦◦◦+- +-+-+-(b) Electrons and ion pairs createdby ionization (t ∼ ns).·◦◦◦◦◦++++----(c) Electrons drift towards the sensewire, ions are very slow by compar-ison (t ∼ 10 ns).·◦◦◦◦◦++++- ---???(d) Electron from the closest ion-ization creates an avalanche at thesense wire (t ∼ 10 ns).Figure 1.1: Illustration of the ionization, drift, and avalanche process.The figures show half of a drift chamber cell, with the sensewire on the left and field wires shown as open circles. The starsrepresent ionization sites, and the + and - symbols representcharges (not necessarily single electrons or ions).7·◦◦◦◦◦++++- --+++(a) Remaining electrons continuedrifting, cloud of ions remains atsense wire from avalanche (t ∼10 ns).·◦◦◦◦◦++++- --+++???(b) The remaining electrons alsoavalanche. Lots of ions are presentat the sense wire (t ∼ 100 ns).·◦◦◦◦◦++++++++++(c) Electrons are gone, ions continueslow drift towards field wires (t ∼µs).·◦◦◦◦◦+++++++++++++++++++(d) The ions continue to drift untilthey hit the field wires (t ∼ 10µs).Figure 1.2: Continued illustration of the ionization, drift, andavalanche process from Figure TrackingIf the drift properties of the gas are well-known (from calculation, simu-lation, or previous experiments), then the recorded signal can be used toinfer information about the original high-energy charged particle. The mostimportant of these is the time-to-distance relation: it is the distribution ofarrival times for signals from high-energy particles passing at a given dis-tance from the wire. If this is known, then a recorded signal can be used toinfer how far the particle passed from the wire. The time-to-distance relationdepends mostly on the gas composition and wire voltages, but also on theoperating pressure and temperature of the drift chamber. Other examplesof useful gas properties are diffusion coefficients and ion mobilities.The arrangement of the wires in a drift chamber is tailored to the re-quirements of the experiment. Most often this is a regular grid of “cells”where a single high-voltage wire is surrounded by low-voltage wires (seeFigure 2.3 for a diagram). The high-voltage wire in the centre of each cellthrough which currents are induced by the motion of electrons and ions iscalled a sense wire. The low-voltage wires are typically not instrumented asthe ions do not create avalanches.With a sense wire grid and a time-to-distance relation, the arrival timesof the signals in all the cells crossed by a high-energy charged particle can beused to track a particle. Schematically, each individual sense wire’s arrivaltime allows us to draw a locus of points or contour around the wire withthe corresponding distance. The path taken by the particle is the line orcurve that comes the closest to being tangent to all the contours simultane-ously. Normally such a path would be required to be a straight line (e.g.,Figure 7.8). Often drift chambers are operated in a strong magnetic field,which causes the charged particles to take helix-shaped paths. The radiusof curvature of a particle’s trajectory gives a measure of the particle’s mo-mentum, so this is highly desirable. Unfortunately the magnetic field alsomakes the drifting electrons inside the gas follow curved paths, so the designand calibration of the chamber is more complex.The time-to-distance relation only gives information about the track in9the two dimensions perpendicular to the wire. From it and an arrival time,we determine the absolute distance from the sense wire of the charged parti-cle’s path through the cell. In general there is a full cylinder (or cylinder-likecontour) around the wire that the track could touch. Two single-wire tech-niques are used to also determine where the charged particle passed alongthe axis of the wire itself (the so-called z-coordinate), and a third techniqueuses the information from multiple wires at the same time.The first involves instrumenting both ends of the sense wire. The signalsfrom a charge cluster hitting the wire propagate in both directions, butbecause the long sense wire has electrical resistance, the signal on each sideof the wire will have a different amplitude (see Figure 1.3). The ratio of theamplitudes of the signals at the two ends of the wire gives a measurementof distance of the ionization event along the sense wire. A downside ofthis technique is the requirement of electronics on both ends of each driftchamber wire.The second technique involves instrumenting only one end of the wireand deliberately letting signals reflect from the far end of the drift chamberback to the instrumented side (see Figure 1.4). The delay between thefirst signal and its reflection can be used to deduce the distance along thewire. This technique is less effective than the former because the reflectedsignal may be ambiguous when multiple clusters are involved, but it has theadvantage of needing no additional readout electronics.The third technique involves combining information from multiple wires.If the wires are not laid out all parallel to each other (so-called axial layout),then which specific cells are traversed by a charged particle will dependon the distance along the general direction of the sense wire axes. Thistechnique (called stereo layout) is often used, because it has no drawbacksduring operation. It does complicate the design and construction of thechamber however.Another method ignores the wires and instead uses instrumented cath-ode strips on the inner and outer shells of the drift chamber. These stripsare aligned to measure the z-coordinate independently of the drift chambersignals. Such a technique was employed for example by the CLEO [13] and10Figure 1.3: Illustration of the charge division technique. In the up-per picture, back-to-back signals are created at a point on thewire. In the second picture, the signals have arrived at the in-strumented ends, and the signal strength is attenuated basedon the distance travelled.Belle [14] detectors.A final method for determining the z-coordinate is simply to use anadditional detector for that purpose. If this extra detector is also a driftchamber, it is called a “Z-chamber”.1.3.2 Particle IdentificationWhile tracking relies on a good understanding of the drift of electrons andions in the gas, particle identification depends on understanding the ioniza-tion behaviour of the gas. The probability of ionizing a gas particle dependsalmost entirely on the speed of the charged high-energy particle in the cham-ber. This is represented by the Bethe formula[15, 16] which describes howmuch energy is deposited in the gas by the passage of the particle:11Figure 1.4: Illustration of the time delay technique. In the upperpicture, back-to-back signals are created at a point on the wire.The signal propagating towards the instrumented end of thechamber arrives at time t1. The reflection off the far end of thechamber reaches the instrumented end at time t2.〈−dEdx〉= Kz2ZA1β2[12ln2mec2β2γ2WmaxI2− β2 − δ(βγ)2]. (1.1)In the above formula, Z and A are the atomic number and atomic massof the atoms in the gas, K is a combination of physical constants, and z isthe charge of the high-energy particle (in units of the elementary charge).me is the mass of the electron, c is the speed of light, β is the speed of thehigh-energy particles in units of c, andγ =1√1− β2 (1.2)is called the Lorentz factor. I is the mean excitation energy of the gas atoms(I ≈ 10 eVZ), and δ(βγ) is called the density correction. The density cor-rection becomes important only at very high energies and is more important12for higher-density absorbing materials like liquids and solids than for gases.Wmax is the maximum kinetic energy that can be imparted on a free electronin a single collision by the high-energy particle. Wmax depends very slightlyon the mass of the high-energy particle, but this is only relevant at veryhigh energies.For the typical particle energies expected in the drift chamber of aflavour-physics experiment, the Bethe formula depends on β2 alone, theother terms being essentially constant. If the momentum p of the particle isknown, for example from measuring the curvature of its tracks in a magneticfield (as described in Section 1.3.1) or from another detector, then the massm can be determined:pc =mc2β√1− β2 . (1.3)The mass uniquely determines the kind of particle.The probability of ionizing a particle determines how many ionizationevents will occur within the boundaries of a cell. Each ionization eventwill liberate one or a few electrons which drifts and creates an avalanche.The recorded signal is the combination of the charge clusters from all theionization events. Thus the number of clusters or the integrated signal canbe used to determine the particle’s type. With a fixed input impedance Ωfor the data acquisition, the integral of the signal over time is the chargedeposited on the wire.1Ω∫V (t)dt = C (1.4)The traditional method of particle identification is to use the integratedcurrent, as this is simple to perform (and can even be done before digitiza-tion using analog electronics). A particle crossing a drift chamber will ionizegas in multiple cells along its track, so to improve the resolution, the chargesfrom all the cells in a track are added up and averaged over the track length.Even with many cells in a track, the difference in the sum of signal integralsbetween different types of particles can be relatively small. Unfortunatelythe charge-per-unit-track-length statistic cannot be used directly, because13x0 10 20 30 40 50 60 70 80 90 100TMath::Landau(x,2,1)3−102−101−10Figure 1.5: Plot of a Landau distribution plotted with parameters µ =2, σ = 1 using ROOT’s TMath::Landau numerical calculation.Note that µ and σ are not the mean and standard deviation.The µ parameter determines the location of the peak (mostlikely value), while σ controls the follows a difficult-to-use distribution. The probability density function iscalled a Landau distribution and one of its features is that the mean andstandard deviation are not well-defined (see Figure 1.5 for an illustration).The calculations for the mean, standard deviation and indeed all of its mo-ments are divergent (they are infinity). With Normal-distributed quantities,one would ask “how close is this particular measurement to the mean valueof this quantity, in units of the standard deviation?” With the Landaudistribution, there is no obvious way to do it, so alternate methods of quan-tifying the data must be used. The divergent mean and standard deviationof the Landau distribution are due to rare large fluctuations that contributeto the sums and integrals in the calculations.The reason that the total charge statistic follows a Landau distribution14is because it results from the combination of several physical processes. Theinitial ionization is a Poisson process, so the number of individual ioniza-tion events (each contributing a cluster of charge) follows a well-behavedPoisson distribution. Each primary ionization can also release multiple elec-trons. Though the most likely number is one, there can be a reasonableprobability that up to a few electrons are released at a time [12]. Theprecise distribution depends on the drift chamber gas and incident particleenergy. In addition to all this, the primary electrons that are produced inthe ionization by the passage of the charged particle can sometimes haverather large momenta. These are called “delta rays”, and can travel a shortdistance in the drift chamber cell and make their own “secondary” ioniza-tions. The electrons from the secondary ionization also go through the driftand avalanche processes, and appear indistinguishable from primary signals.The derivation of the theoretical deposited charge involves the convolutionof all these processes, and generally includes integrals over the number ofelectrons released and over electromagnetic frequencies up to infinity. In areal physical situation obviously there are limits on these quantities, but thisdoes not change the qualitative statement that large rare fluctuations pre-vent the use of simple statistical treatments. The empirical measurement ofthe deposited charge is well-modelled by a Landau distribution, if you havea cut-off of some kind (e.g., a histogram with finite range).A robust method to deal with the Landau-distributed quantities is toperform a so-called “truncated mean”. Instead of using the total chargeof all the signals per unit track length, first the individual charges fromthe different cells are sorted and only the values below a certain percentilerank (typically ∼ 80%) are used. The rest of the values are discarded,and these will contain the large-but-rare fluctuations from the delta rays.The resulting truncated mean statistic is well-behaved and can be easilyanalyzed. Unfortunately this method necessarily throws away information,effectively reducing the number of cells that can contribute to the chargemeasurement.An alternative to the deposited-charge statistic is the number of clus-ters. This skips the variations due to the number of primary electrons and15the amplification process, so the statistic should be well-behaved. Unfortu-nately resolving the clusters can be difficult, as the electronic signals frommultiple clusters can pile up and look like large-amplitude single clusters.Further, spurious noise in the signal can fool the cluster-counting algorithmsinto counting fake clusters, and some algorithms may be too complex to runonline (i.e., as fast as the events are read out in the detector). The choiceand tuning of the cluster-counting algorithm is critical to obtain good per-formance. Certain design choices can make this process easier, for examplefewer clusters will pile up if a gas with a slower drift velocity is chosen.Once a suitable statistic is found (either truncated mean of the depositedcharge per track length or number of clusters per track length), it is a sim-ple matter to build up distributions of these quantities for different particlespecies. This can be done by using known radiation sources or processes inwhich the particle identities are known, or an existing particle identificationdevice such as a time-of-flight counter. A time-of-flight counter consists ofa pair of charged particle detectors placed a large distance apart so that thetime delay between the coincident signals is measurable. The distance be-tween the detectors is measured precisely, so the time delay is converted intoa speed. With a known particle momentum (e.g., from a bending magnet,tracker, or from the source), the speed gives the mass and thus identity ofthe particle.Once one has validated distributions of the truncated mean of the de-posited charge or number of clusters for the various relevant particle types,one can measure the same statistic for an unknown particle and assign alikelihood of being a given particle. For drift chambers, the only relevanttypes of particles are electrons (and positrons), protons (and antiprotons),deuterons, charged pions, muons, and kaons. Other charged particles arenot long-lived enough to leave measurable tracks in the detector. Depend-ing on the energy range, possibly only one or two particle species may berelevant, simplifying the analysis.16Chapter 2Design Considerations ofDrift Chambers2.1 Overall DesignDrift chambers are general-purpose detectors of high-energy charged par-ticles, but each is designed with a specific experiment in mind. They aretypically one-of-a-kind, designed and custom-built by researchers and tech-nicians in particle physics and are not commercially produced by compa-nies (like e.g., photomultiplier tubes). The various design choices are madeconsidering the requirements of the experiment at hand. Because of thedependence on these details, the range of designs of drift chambers that canbe found in the literature is quite broad.For SuperB and the prototypes used in this work, the primary designconsideration was the amount of material. Because of the types of analysesdone with B-factory data, very precise identification and determinationsof tracks of charged particles with ∼ 1 GeV/c or less momentum is veryimportant. The main source of uncertainty in these measurements is theelastic scattering of the charged particle on material in the drift chamber.The term used is “multiple scattering” because often there are multiplesuch scatterings. Multiple scattering also affects the measurements madeby other detector components, because it changes the momentum of the17Figure 2.1: Schematic of a planar chamber layout. Taken from [12]where it is Figure 11.2, on page 364.particle while it is traversing the drift chamber. The material involved iseverything in the drift chamber: the gas, the wires, and the external casing,and even the front-end electronics.There are a few canonical categories used to describe drift chamber de-signs, and three of which will be described here.Planar chambers feature just one (or just a few) layer of sense wires (seeFigure 2.1). Since a single high-energy particle will likely only excite onecell, a single planar chamber cannot be used for tracking by itself. Theyare often stacked (with the wire orientations orthogonal) or combined withother detectors (see [17] for an example).Jet chambers have sense wires arranged in “rays” or “spokes” to bettercapture the signals left by jets of particles coming from the hadronization ofhigh-energy quarks and gluons. In a jet chamber the cells are rather wide,so a low-diffusion gas and high electric fields are needed. An example jetchamber design can be seen in Figure 2.2.Cylindrical drift chambers with a “small cell” design have become stan-dard for flavour physics experiments. An example is the ARGUS drift cham-ber, whose cell layout can be seen in Figure 2.3. The small cells measurearound 1 cm on each side and are designed to “tile” nearly the whole cross-section of the drift chamber gas. Counterintuitively, drift chambers with18Figure 2.2: Schematic of the OPAL Central Jet Chamber. The figureon the left shows the arrangement of the radial sections. Thefigure on the right shows the individual wires in part of a section.Taken from [18].small cells require less material than large-cell chambers, even though thenumber of wires is greater. This is because other designs like jet chambersrequire high electric fields far away from the wires in the large cells, so thewires are made thicker to avoid having spontaneous ionization of the gasby the electric field near the wire surface. The thicker wires need highertension to reduce gravitational sag, and thus the endplates must be thickerand stronger as well. Small cells have other advantages: electron diffusionis less important because it is proportional to the drift distance; the chargeaccumulation on each wire is lower, delaying ageing; the tiling effect of thesmall cells reduces the amount dead space in the detector; and the lowertension in the wires means result in less creep.Creep behaviour of the wire material should be well-understood. Creep is19Figure 2.3: Schematic of a cylindrical chamber layout for the ARGUSdrift chamber. The empty circles are the sense wires, and theblack circles are field wires. This configuration is identical tothe one planned for SuperB. Taken from [12] where it is Figure11.14, on page 380.the slow permanent deformation of a material experiencing sustained forces.In the case of a wire, the creep effect would be to slightly lengthen, loweringthe tension and increasing the gravitational sag. To compensate for materialcreep the wires are given extra tension upon stringing so that they have theproper tension after a certain expected amount of creep. More details aboutcreep are given in Section Gas CompositionGenerally drift chambers use a mix of gases, the major component typicallybeing a noble gas. The minority component(s) is typically a simple hydro-carbon (e.g., ethane) or carbon dioxide, and is called a “quencher”. Theprocess of ionization produces ultraviolet photons, which can cause unde-sired further ionization via the photoelectric effect. The quencher’s role is to20absorb these ultraviolet photons, so quencher gasses are chosen to stronglyabsorb ultraviolet radiation. The ratio of the gas components varies quite alot, from 50 : 50 [17] to 97 : 3 [19]. Sometimes additional minor gas compo-nents are added, usually to address ageing. For example it is believed thata small component of water vapour helps reduce or temporarily reverse theeffect of drift chamber ageing. See Section 2.5 for more details.A traditional primary gas of choice for drift chambers is argon, but driftchambers that need to minimize multiple-scattering now use helium as theprimary gas, as it is the lightest monatomic gas. Helium unfortunatelyhas a high electron diffusion constant (i.e., the amount that the electronsdiffuse per unit drift time), so it must be used with a small-cell designto minimize the total diffusion [20]. Helium has a much higher ionizationpotential than argon, the downside of which is that higher wire voltages arerequired to create measurable avalanches on the sense wires (the electronsmust be accelerated to higher momenta before ionizing more atoms). Itwas revealed with some surprise that good results could be obtained froma helium-based drift chamber [21]. A benefit of helium’s higher ionizationpotential is that the low-energy photon background from the beam has asmaller chance of triggering an avalanche and being registered as a signal.For high-rate environments such as flavour factories this is essential [22].To illustrate how helium can reduce multiple-scattering, consider thatthe momentum resolution of a charged particle with momentum p can bewell-parametrized by a function of the following form [23]:σpp2=√A2 +(Bp)2). (2.1)Momentum resolution is reported as the uncertainty on a momentum mea-surement σp divided by the square of the momentum p. This is because theuncertainty of the momentum measurement generically is proportional top2, so the ratio better shows the dependence on other factors [12]. In Equa-tion 2.1, A is the fixed contribution from the measurement errors like timeresolution and wire position. For an argon-based gas, A is typically around210.5 to 1.0 %/GeV, while for helium-based gases it can be significantly worse.The second term with B is the contribution from multiple scattering, and isinversely proportional to the momentum of the charged particle. B for anargon-based gas is typically around 0.7%, but for a helium gas it is around0.3%.For high momentum p, the dominant contribution to σp/p2 is from thefirst term, so the difference in B values is negligible. Thus drift chambersbuilt to detect very high energy particles will use a gas mixture based on its Avalue. In flavour-factory experiments like SuperB, most charged particles tobe detected have lower energies (less than 1 GeV/c), so the B contributioncan be dominant. Most flavour-factory drift chambers use helium as theprimary gas component because it has a smaller B value even though its Avalue is worse than argon.2.3 Wire MaterialsSeveral materials have been used for drift chamber wires. The materialsmust be non-magnetic in order to not react to the external magnetic fieldthat allows us to measure particle momenta. They also need to be strongenough to avoid breaking, because some tension is applied to minimize thegravitational sag. The wires should be conductive enough to carry the rawelectronic signals to the external electronics, and should not react with thegas.As mentioned in Section 2.2, multiple scattering is only a concern forflavour-factory drift chambers, as another process dominates the momen-tum resolution at higher momenta. In argon-based drift chambers for whichmultiple scattering is not a concern, the gas alone contributes so much mate-rial that the wire’s material is negligible. For helium-based drift chambers,the material in the wires is quite significant.The “creep” behaviour of the material should be well-understood. Creepis the slow permanent deformation of a material experiencing sustainedforces. In the case of a wire, the creep effect would be to slightly lengthenthe wire, lowering the tension and increasing the gravitational sag. To com-22pensate for creep the wires are given extra tension upon stringing so thatthey have the proper tension after a certain amount of creep. Creep isa bigger factor in aluminium wires than other materials, and experimentsusing aluminium wires generally do a study of the creep behaviour duringdevelopment [24].The material used for sense wires and other wires is generally different.Sense wires must be very thin in order to generate strong electric fieldsnear their surface for electron multiplication. The field wires are typicallymuch thicker so that the surface fields are smaller to prevent the onset ofthe Malter effect (see Section 2.5). The thin sense wires must be made ofstronger and more conductive material, since mechanical strength and con-ductivity both decrease with wire diameter. The mechanical and electricallimits to the sense wire diameters are about 20µm [25]. Thinner than this,the wires are difficult to string and tend to break when attached to thefeedthroughs on the endplates. Thinner wires having higher electrical resis-tance may be advantageous for the charge-division method of determiningthe z-coordinate [26].There are a few canonical wire materials used in drift chambers. Thematerials used in a few historical drift chambers are shown in Table 2.1.Stainless steel and copper-beryllium alloys are used because they have sim-ilar thermal expansion coefficients to aluminium [25]. Aluminium is thetypical material used for endplates and supporting structures, and havingthe whole chamber expand and contract at the same rate during tempera-ture fluctuations is obviously desirable. Unfortunately stainless steel is notnormally antimagnetic, so special non-magnetic wires must be obtained [27].For small-cell low-mass drift chambers, the canonical material of choicefor the sense wires is gold-plated tungsten-rhenium. The tungsten-rheniummaterial has high strength, can be made into very thin wires, and has ac-ceptable creep characteristics. Gold coating is needed to improve the con-ductivity for the electronic signal and to provide a non-reactive surface.The Italian prototype proto 2 used in this study had six layers of cellswith molybdenum sense wires instead of tungsten-rhenium (Figure 5.1).Molybdenum has roughly the same mechanical properties as tungsten-rhenium,23Table 2.1: Table of wire materials used in the drift chambers of varioushistorical experiments.Experiment Sense Wire Field Wire NotesISR Final Design Ni-Cr High resistivity for charge di-vision [26]ISR Initial Design 25µm stainlesssteel100µm Cu-Be High-resistivity sense wire forcharge division, special non-magnetic stainless steel [27]UA1 35µm Ni-Cr 100µm Au-coated Cu-Be[28]ARGUS 30µm W 76µm Cu-Be76µm fieldMajority of scattering is fromthe gas [19]CLEO-II 20µm Au-coated W100µm Au-coated Al andCu-BeAl for inner layers, Cu-Be forouter to save money, as Aluwire is expensive [29]CLAS at CEBAF 20µm Au-coated W150µm Au-coated Al[30]KEDR 28µm Au-coated W150µm Au-coated Ti[31]CDC at SLD 150µm Au-coated AlSense wires unspecified [32]but has much lower density and electrical resistivity. The density of molyb-denum is nearly half that of tungsten, and tungsten’s resistivity is roughly9.5µΩcm [33] while molybdenum’s is 5.3µΩcm [34]. Though the gold coat-ing carries much of the signal, a lower-resistivity wire material may be ben-eficial. The other two layers in the eight-layer prototype were the canonicaltungsten-rhenium for comparison. No detailed study of the performance ofthe molybdenum cells in proto 2 was performed. Only one other drift cham-ber seems to have ever used molybdenum wires: the inner drift chamberfor the TOPAZ experiment at TRISTAN [35]. Only the TOPAZ field wiresare molybdenum, the sense wires are the more standard tungsten-rhenium.They do not state their reasons for the choice of molybdenum, but it doesnot appear to be for the minimization of multiple scattering based on thekinds of experiments done at TRISTAN.24The canonical choice for field wires is larger-diameter aluminium. Largediameters are used to avoid the Malter effect (Section 2.5). Aluminiumis chosen because it has a low density for a metal, so the large-diameterwires contribute less material. Most experiments use gold-coated aluminium,for conductivity and to provide an inert surface. BaBar used gold-platedaluminium, and Belle used bare field wires. Bare aluminium wires tend tohave more surface defects and are subject to oxidation, but no conclusiveanalysis has been done to determine whether the gold coating is significant.Belle’s experience shows that the gold coating is not essential, and the goldcoating contributes a non-negligible portion of the total material of the wires.Belle-II is continuing with bare aluminium field wires, and SuperB was alsodesigned to use bare wires.2.4 Outer StructureThe outer structure of a cylindrical drift chamber consists of the inner sup-port tube, the exterior barrel, and the endplates (see Figure 2.4). The outerstructure provides the physical structure to hold the wires, provides a gasseal, and provides a grounded electromagnetic shield for the inside of thechamber.Because of the large number of wires under tension (typically thousands),the structure has to resist forces on the order of tonnes, even if each wirehas a reasonable tension on the order of grams.The endplates of large drift chambers are commonly made of aluminium,but some are made of composite materials like carbon fibre. A finite-elementanalysis is done of the endplate deformation in order guarantee that thestructure will not collapse, and in order to adjust wire tensions to accountfor a changing endplate position and shape as more wires are attached. Theshape of the endplates also varies: some are flat, some conical or hemispher-ical, and some with wedding-cake-like steps [36].The outer cylinder is always load-bearing, and takes most of the forcefrom the endplates. Typical materials are again aluminium or carbon fi-bre. A construction strategy must be devised to hold the endplates during25Figure 2.4: Photo of the BaBar drift chamber during construction.The inner cylinder and endplates are visible, as is the externalmechanical support for the endplates (the blue claw-like pieces).The outer cylinder plates are being installed, after which theexternal supports will be removed. Photo from Chris Hearty.Figure 2.5: Example of two endplate designs considered for SuperB.The design on the left has concave spherical endplates, whilethe one on the right is a stepped “wedding-cake” design. Takenfrom the SuperB Technical Design Report [37]26stringing before the outer cylinder can be attached. For example externalstruts may be attached to support the endplates. After stringing, the strutsare removed as the outer cylinder plates are attached.The inner cylinder of the chamber is sometimes load-bearing, but some-times it is only a ground plane and gas seal. In some designs, the innercylinder is the beam-pipe itself. Even for load-bearing designs, the materialtends to be thinner and lighter, such as carbon fibre or porous aluminiumcells. BaBar used a beryllium inner cylinder [38]. Beryllium is a strongmaterial that has a remarkably long radiation length (the average distancethat particles will travel before interacting), but is difficult to machine andits dust is extremely toxic. Non-load-bearing inner cylinders may consistsimply of a conductive foil (e.g., aluminized mylar) for grounding and gassealing.2.5 AgeingAgeing is a term used to describe the gradual degradation of the performanceof a drift chamber over the lifetime of an experiment. The observable phe-nomena are: a reduction in the gas gain when operating parameters thataffect the gas gain are held constant (e.g., the wire voltages and gas com-position) and persistent currents on the wires in the absence of traversingparticles. A consequence of lower gain is lower-amplitude signals relative tothe intrinsic noise of the system, and thus reduced accuracy of measurementsof the signal arrival times and charge integrals. When threshold algorithmsare used (e.g., for arrival times and cluster counting), the thresholds selectedat the beginning of the experiment may be too high after some ageing hasoccurred, spoiling all the measurements. The information in this sectionis mostly taken from an extensive review of drift chamber aging by JerryVa’Vra at SLAC [39]. Research is ongoing on understanding ageing, bothfrom a microscopic perspective [40] and from a pragmatic perspective [41]that wishes only to mitigate it. During the beam tests described in thisthesis, ageing tests were performed by Rocky So. The work forms part ofhis PhD thesis [42].27The mechanism of ageing is complex, but can generally be understood asa buildup of material on the sense and field wires. During normal operationof the drift chamber, there is a lot of ionization of the gas from primary andsecondary ionizations, and the avalanche process. For most drift chambergas mixtures, the ions of the main component (argon or helium) are non-reactive, but the ions, fragments, and radicals from the quencher gases canparticipate in rather complex chemistry. Contaminants in the gas will alsoplay a role, if present (e.g., outgassing molecules from a glue or cleaningproduct). For example, polymers can form from the fragments of broken-uphydrocarbon molecules. The final products will accumulate on the surfacesinside the drift chamber: the wires and the outer structure.The build-up of material on the drift chamber inner surfaces can haveseveral effects. On the very thin wires, the material can effectively increasethe wire diameter. The material build-up is typically non-conductive, socharges arriving from ionization processes can build up and slowly diffusethrough to the metallic surfaces below. In all these cases, the result is areduced signal amplitude from smaller avalanches and insulated conductors.The extra material may also increase the gravitational sag of the wire.This is likely negligible, as the wire masses are ∼ 10 − 100 mg and thedeposits are negligible. No study has yet examined this possibility.Extreme cases of ageing can result in so-called “dark currents”. Theseare persistent currents in the wires of a drift chamber even when no high-energy charged particles are crossing the chamber. The mechanism causingthese dark currents is called the Malter effect [43]. The effect is that thenon-conductive coating on the cathodes (the electrodes towards which theions drift, i.e., field wires) prevents the ions from being collected by thecathode. The positive charge thus accumulates and attracts electrons frominside the cathode. If the electric field around the cathode and the positivecharge buildup is strong enough to overcome the work function of the sur-face, these electrons are ejected into the gas rather than recombine with theions. The electrons then drift towards the sense wires and cause avalanches,releasing more ions. This self-sustaining and self-amplifying process explainsthe currents which are present even without high-energy particles crossing28the chamber.Since ageing is produced by the ionization process in the chamber, theduration is quantified using “deposited charge” accumulation: the totalamount of charge deposited on the sense wires per wire length. This meansthat drift chambers operating in high-rate environments will age faster, allother things being equal. Ageing is a primary design consideration for driftchambers intended for high-rate experiments or that will operate for a longtime [44].The chemical deposits responsible from ageing come from the ionizationof the quencher, so a smaller quencher fraction is likely to reduce the rateof ageing. Some quencher is always needed as described in Section 2.2,so it cannot be eliminated entirely. The choice of quencher may also beimportant, but among the lower hydrocarbons (methane, ethane, propane,butane, the most common quenchers) no differences are observed.Larger wire diameters provide a larger surface area for the material tobuild up, which would reduce the ageing effect. Unfortunately thicker wireswould mean more tension is needed (and thus stronger endplates and outerstructure), and higher operating voltages would be needed to provide thesame gas gain. Unless the material is changed, thicker wires also increasethe amount of material in the chamber, leading to more multiple scattering.The overall gas flow rate can influence ageing. Some materials like plas-tics and glues can slowly release contaminants into the drift chamber volume.A drift chamber or its gas system may also have hard-to-detect leaks wherecontaminants can enter. Thus most chambers continuously flow gas throughthe chamber, filtering and re-circulating some of the gas. As an example,the BaBar drift chamber flowed 15 L/min of gas, of which 12.5 L/min wasrecycled and filtered [38]. The BaBar drift chamber was also kept at a small4 mbar pressure above the ambient atmosphere so that any leaks would beto the outside, thus preventing contamination. Sealed gas ionization detec-tors do exist (e.g., [45]) but they require careful sealing procedures andhigh-purity gases.Small quantities of impurities in the gas are observed to have significanteffects on ageing [39]. Some of these impurities can have positive effects, by29delaying or even apparently reversing the ageing effect. There is a bit of folkwisdom associated with these additives, as some were discovered by accidentand not systematically studied. For example it is thought that molecularoxygen in the gas can combine with hydrocarbon radicals to produce non-reactive molecules. Similarly the addition of water vapour is thought to“reverse” the effect of ageing by embedding itself in the insulating depositson the wires and increasing their conductivity [41].An example of ageing can be found in the report of the performanceof the BaBar detector [46]. Over the lifetime of the BaBar experimentthe drift chamber wires accumulated ∼ 34 mC/cm of charge, and the gain(after adjusting for changes in voltage) was observed to drop by 0.337 ±0.006 %/(mC/cm). To compensate, the voltages on the sense wires were in-creased periodically to maintain roughly the same gain. The voltages cannotbe increased arbitrarily, as the wires interact electrostatically with the fields.The effect is that the wires’ gravitational sag is enhanced by large voltages,and the sag can be large enough to break the wire or make it touch otherwires. The effect depends on the wire tensions, but the voltages required forinstability are on the same order as the typical operating voltages [12].30Chapter 3SuperB3.1 IntroductionCutting-edge accelerator-based high-energy particle physics experiments canbe classified into two types. So-called “energy-frontier” experiments collideparticles at heretofore-unreached centre-of-mass energies or energy densi-ties [47]. A popular example of this approach is seen in the ATLAS and CMSexperiments at the LHC, where protons or ions are collided at the highest en-ergies ever obtained in a laboratory. Modern energy-frontier experiments arehuge enterprises, involving entire consortia of countries and requiring signif-icant industrial support. The LHC and its experiments are among the mostcomplex machines ever constructed by humanity. It is admirable that thesemachines are not used for war, as with many other devices in this category.There are real technical, economic, and political reasons why energy-frontierexperiments are difficult to improve. Other examples of energy-frontier ex-periments include the Tevatron[48] and the cancelled Superconducting SuperCollider[49]. The only currently planned future energy-frontier experimentsare China’s Circular Electron Positron Collider (CEPC [50]) and the Inter-national Linear Collider (ILC [51]). The ILC has been in planning stagesfor decades, and some consider it an eternally-hypothetical experiment thatmay never be built.The other type of cutting-edge particle experiment is the so called “intensity-31frontier” type [52]. Rather than trying to directly reach the energies requiredto produce new particles or unlock new physics processes, high-precisionmeasurements are made of reactions at more moderate energies but at ex-tremely high rates. Through higher-order interactions and virtual particles,currently unobserved particles and unknown new physics can contribute tothe results. A famous example of this is the ARGUS experiment being ableto constrain the mass of the at-the-time undiscovered top quark despite notbeing able to produce real top quarks[53, 54]. If there are indeed new physicsprocesses or particles, their presence would slightly shift the values of reac-tion rates from those expected under the regular standard model. In orderto measure these slight shifts, lots of data are required, hence the focus onhigh-precision measurements at high rates. Intensity-frontier experimentstend to be of a much smaller scale than energy-frontier ones, capable ofbeing undertaken by single countries (albeit only rich first-world countries)and by consortia of universities. Examples of intensity-frontier physics arethe BaBar and Belle experiments, which focused on the production of Bmesons to study CP violation and other flavour physics topics.SuperB was a planned particle physics experiment of the intensity-frontiertype led by the national Italian particle and nuclear physics institute, theInstituto Nazionale di Fisica Nucleare [55]. It was to be a so-called super-flavour-factory, and a showcase of new technologies designed to tease outthe details of physics beyond the standard model. One of the repeated pro-motional phrases was that when high-energy experiments (e.g., the LHC)find evidence of new physics, SuperB will ascertain exactly what kind of newphysics has been found.SuperB was to be the successor to BaBar, and indeed would have re-used some of the components of the detector, and many senior scientistsfrom BaBar were involved in the planning and design stages of SuperB. Un-fortunately during these initial stages of the project, the budget balloonedto 1 billion euros from an original estimate of 350 million, and the newly-appointed Italian government cancelled the project. Much work was donebefore the cancellation in predicting the physics results obtainable with Su-perB (e.g., [56]), and many prototype components were designed and con-32structed [37, 57–59].A successor to Belle is currently being developed in Japan, called Belle II.Compared to SuperB and BaBar, Belle II is a less ambitious upgrade of Belle,but it has the advantage of being in the same location as its predecessor andundertaken by a country in a better financial situation than Italy. It is lessambitious in the sense of mostly following the design of the original Belleexperiment with incremental upgrades [60]. In comparison, SuperB was tobe in a different country than its ancestor, was to be built at a brand-newfacility with a new accelerator using new technology [61], and had significantchanges in its design.3.2 SuperB Drift ChamberFrom the original conception of SuperB until its cancellation, much initialwork was done to determine the overall design and features of the acceleratorand detector. The most detailed description can be found in the TechnicalDesign Report [37]. Much of the design was inherited from the experienceof the BaBar [38] and Belle [14] experiments.For example BaBar found that the hexagonal cells combined with thesuper-layer design resulted in unnecessary dead space between layers. Deadspace is a region of gas with no associated sense wire, and does not con-tribute to the measurements. The SuperB drift chamber was designed tohave square or rectangular cells to mitigate this, but the trade-off is thatthe time-to-distance relation has more severe dependence on the track angle.Another example is the material chosen for the field wires. In the BaBardrift chamber, gold-coated aluminium wires were used because it was as-sumed that the surface of bare aluminium wires would be too rough andwould cause premature ageing of the chamber. Belle used bare aluminiumwires and observed no such effect, and thus had a reduced amount of ma-terial in the drift chamber volume, which is highly desirable. Thus theSuperB drift chamber was to use bare aluminium wires too.This section will present those aspects of the SuperB drift chamber whichinfluenced the design of the prototypes used in our studies. Other details33about the construction, electronics, cooling, high-voltage, and structural in-tegration into the detector can be found in the Technical Design Reportand are not repeated here. The SuperB project was cancelled before a finaldesign was chosen for the drift chamber, so some choices were still prelimi-nary. Most design choices were optimized using simulation programs (eitherGEANT or a SuperB -specific program called FastSim).The SuperB drift chamber has three purposes: to precisely measure themomentum of charged particles (see Section 1.3.1), to identify said chargedparticles (see Section 1.3.2), and to provide a trigger for the whole experi-ment. The charged particles involved generally have momenta around or be-low 1 GeV/c, even though the centre-of-mass energy of the colliding beamsis ∼ 10 GeV. This is because the very massive resonances and particlescreated at the interaction point are very short-lived, and the only parti-cles that make it to the drift chamber itself are daughters possibly several-generations-removed from the original. All these daughter particles sharethe energy budget (along with neutral particles that are not detected bythe drift chamber), bringing us into the sub-GeV range. This is also whycharged particle identification is very important, because the original par-ticles are only observed through reconstruction by adding up the momentaof the daughter particles which are actually observed in the detector. If asingle particle in the drift chamber is misidentified, it can completely spoilthe inferred measurements of the parent particle.Because the majority of particles to be detected have momenta around1 GeV/c, the dominant contribution to the uncertainty of measurementsmade in the drift chamber is from multiple-scattering. Multiple-scatteringis when the charged particle crossing the drift chamber interacts elasticallywith the material in the chamber. The material may be from the outer shell,end-plates, wires, or gas (see Figure 2.4 showing the different components).The elastic interaction means that no new particles are created, but thecharged particle exchanges a bit of momentum with the material that ithits. This causes a slight kink in the track, or a slight change in energy.Multiple elastic scattering thus makes the tracks jagged and not conformingto our helical expectations, and spoiling the momentum measurement. Most34of the design choices for the SuperB drift chamber were made with the aimof reducing the amount of material in the chamber in order to minimizemultiple scattering. Reducing multiple scattering also helps those detectorcomponents outside the drift chamber, because the momentum of particlesis less affected by crossing the drift chamber. Another benefit is that thewhole structure actually has a reduced weight, easing structural constraints.The total length is 3092 mm, but with space allotted for the electron-ics and endplates, the axial wires would be 2557 mm long. The inner andouter radii of the chamber are 270 mm and 809 mm, respectively. These pa-rameters are largely defined by the positions and sizes of the other detectorcomponents such as the vertex tracker and the calorimeter. The inner wallis made of carbon fibre, and the design called for it to be as thin as possible.Convex endplates were determined to allow slightly longer wires comparedto concave, which allows the drift chamber to detect particles with moreextreme angles.As mentioned earlier, BaBar used hexagonal cells. This has the advan-tage of requiring fewer field wires per cell compared to square cells, becauseof the way hexagons pack together. However there are several disadvantagesto the hexagonal cells. The voltages required in a hexagonal configurationmean that thicker field wires need to be used to avoid the onset of the Maltereffect (described in Section 2.5). In a square-cell design, the voltages can bemade lower, because there are more field wires, so the wires can be thinner.A consequence of the thicker wires in the hexagonal cell case is that a greatertension must be applied to achieve acceptable gravitational sag (∼ 200µm).When the tensions of all the wires are added up, the higher-tension butless-numerous wires in a hexagonal configuration actually apply more forceto the endplates than the lower-tension but more-numerous wires. Thus thehexagonal cells would force a design with stronger and thicker endplates andsupporting cylinders.There are other considerations here too: hexagonal cells are closer tosymmetric circular cells, so their time-to-distance relation is more uniformas a function of angle than square cells which have deeper and narrowercorners. A track clipping the corner of a square cell would leave a signal35Figure 3.1: SuperB drift chamber schematic, taken from the TechnicalDesign Report [37]. Dimensions are in millimetres. IP indicatesthe interaction point, while FWD Elect and BWD Elect referto electronic component modules. DCH is drift chamber whileDIRC, FTOF, and FEMC are other detector components.with an unusually long arrival time. BaBar used stereo wire layers (layersof wires not parallel to the drift chamber axis, but rotated by an angle) toprovide a measurement of the z track coordinate, but the hexagonal celldesign does not allow adjacent cell layers to have different stereo angles (thewires would touch). Thus between each layer of cells that changed angle,they had to add a space with no cells and extra “guard” wires to correct theelectric fields in the adjacent layers. This dead space is clearly detrimental,and the extra wires ruin one of the main advantages of a hexagonal layout:the smaller number of wires per cell. A square cell design allows adjacentlayers to have different stereo angles, so although the SuperB drift chamberis roughly the same size as BaBar’s, it is able to support 44 layers of cells36instead of just 40.Since the cell layout is of concentric rings of approximately square cells(or square-ish, given the curvature), the cell sizes must change slightly asa function of radius in order to fit. The cell sizes range from 10.4 mm to19.2 mm, with the smaller cells in the innermost layers. The inner cells aresmaller because they are exposed to higher levels of background particles,being closer to the beam. Smaller cells in the same space means more cells,resulting in a reduced background intensity per cell.The gas chosen for SuperB is a 90 : 10 ratio of helium and isobutane. He-lium is chosen as the primary component because it is the lightest noble gas,and thus minimizes the amount of material in the chamber. Helium has arelatively low electron drift velocity compared to other drift chamber gasseslike argon. With the wire voltages used at SuperB, the electron velocitieswould be “unsaturated”. Saturated electron velocities result when the accel-eration from the electric field is balanced by the collisions with gas molecules,so the electron drift velocity does not vary much with changing electric fieldsand does not fluctuate much with gas temperature or pressure. A mostly-constant drift velocity would make the time-to-distance relations and cal-ibrations much simpler. Nevertheless, the reduction of multiple-scatteringfrom choosing helium supersedes, and the unsaturated gas problem can bedealt with with careful calibration and by controlling the gas temperatureand pressure. A positive consequence of the slower electron drift velocity inhelium is that the charge clusters hitting the sense wires will be more spreadout in time. This makes the job of identifying individual clusters easier, asthey are less likely to overlap.Isobutane is the quencher gas that is responsible for re-absorbing ultra-violet photons released when the drifting electrons ionize the gas, or frombackgrounds related to the beam. Without a suitable fraction of quencher,the photons could propagate and ionize more gas and the whole chamberwould become a Geiger tube. The quencher is nearly always a hydrocar-bon gas, and the specific choice is mostly made based on availability andconvenience.The outer structure of the SuperB drift chamber is made entirely of car-37bon fibre. The outer structure is responsible for supporting the huge forces(2 tonnes, or 19.6 kN) from the wires with minimal deformations, and alsoprovides a gas-tight envelope. The amount of material should be minimizedto reduce the effect on particles that cross into and out of the chamber. Us-ing finite-element analysis programs, it was determined that a convex hemi-spherical shape would minimize the thickness of the endplates, and wouldfortuitously also maximize the lengths of the inner wires, which slightly in-creases the range of particle angles that can be detected. The final design,which includes considerations for the weakening of the endplates by drillingthe holes for the wires, is only 8 mm thick. For comparison, a flat endplatewould need to be 52 mm thick to have the same deformations.The inner cylinder of the SuperB drift chamber is designed to be non-load-bearing in order to minimize the material that particles must cross be-fore entering the drift chamber. Its only role is then to provide gas tightness.The drift chamber operates at atmospheric pressure, but the pressure sealand inner cylinder are designed to accommodate up to 20 mbar of differen-tial pressure to survive rapid weather changes. The 270 mm radius cylinderis composed of a 3 mm thick honeycomb structure sandwiched between two90µm sheets, all of carbon fibre. The carbon fibre sheets are also each cov-ered by a 25µm aluminium foil for shielding against stray electromagneticfields.In addition to providing gas tightness, the outer cylinder must supportthe entire force of the wires against the endplates. In order to allow forstringing of the wires, the cylinder is made of two half-shells, and these willonly be installed after stringing. During stringing, a special external supportframe is used to keep the endplates fixed. See Figure 2.4 for a photo of theBaBar drift chamber during construction, showing the same technique thatwould be used for SuperB. The outer cylinder is structured the same way asthe inner one, but with a 6 mm thick honeycomb structure and 1 mm thicksheets.The final SuperB design called for gold-plated molybdenum sense wires.Molybdenum has roughly the same mechanical strength as the more typi-cal tungsten-rhenium, but has less resistivity and is slightly less dense (see38Section 2.3 for more details). The result is a better-quality signal recordedby the electronics, and 1.6 kN less force on the endplates. The properties ofmolybdenum wires however were not fully explored, so the original conceptfor the Italian prototype (see Chapter 5) was to test the use of molybdenumwires, and more work was needed to test the creep and breaking strengths.The diameter of the sense wires was chosen to be as small as possible whilestill allowing them to be handled for construction. 20µm is the thinnestpractical wire for this purpose. Thinner sense wires allow lower voltagesto be used, which also allow thinner field wires that do not avalanche, andthus less tension and less weight on the endplates. Using molybdenum sensewires increases the radiation length of the whole gas and wire system to545 m from 480 m when using tungsten wires.The field wires are chosen to be 90µm thick bare aluminium wires. Thisdiameter is the smallest that keeps the surface field below 20 kV/cm. Thisis considered a safe value to avoid the Malter effect from manifesting itself(Section 2.5).39Chapter 4Particle Identification StudyThis chapter is a literal embedding of a paper published in 2012 [1]. Thereferences cited can be found in the bibliography at the end of this thesis.The last few sections appeared as appendices in the original paper, so some ofthe references have been modified to suit, along with a few other formattingchanges and typographical corrections. Only a brief overview of the workwill be described here, as sufficient detail is provided in the paper.Two prototype drift chambers were built at TRIUMF. These are single-cell chambers, 2.7 m in length. The cell layout can be seen in Figure 4.2. Ina beam of pi+, e+, and µ+ particles at ∼ 210 MeV the prototypes were testedwith different configurations of: wire diameters, amplifiers, connector cables,and wire voltages. An external time-of-flight (TOF) system was used toprovide unambiguous particle identification. To study particle identification,we constructed “tracks” of 40 cells being crossed by a particle by composing40 single-cell events that were identified to be the same kind of particle bythe external TOF system.The composite tracks were analyzed using a traditional truncated-meanmeasurement of the integrated charge. We also do particle identificationusing cluster counting, and various algorithms are tested. The algorithmparameters are optimized based on the performance on real data.The main result is that cluster counting is found to improve the pionidentification efficiency from 50% to 60% when requiring 90% muon rejection40efficiency, compared to the truncated-mean technique alone. It was foundthat optimal smoothing times are ∼ 5 ns, so that amplifiers and digitizers ofonly hundreds of MHz bandwidth would be sufficient to implement clustercounting (previously it was thought that at least 1 GHz would be required).Secondary results are that all the algorithms tested are equally effective whentheir parameters (thresholds, smoothing times) are properly optimized, andthat attempting to use the cluster times themselves does not improve PIDperformance. Unfortunately the analysis comparing amplifiers, wire choice,and cables was not able to provide good conclusions.4.1 IntroductionThis paper describes the development and testing of a prototype drift cham-ber whose purpose is to evaluate the feasibility of a “cluster-counting” tech-nique [62] for implementation in a high luminosity e+e− experiment. Clustercounting is expected to improve particle identification (PID) by reducing theeffect of fluctuations in drift chamber signals. These are due to gas amplifi-cation and the fluctuation in the number of primary electrons per ionizationsite. There may also be improvements in tracking resolution, but this isleft for a later study. The requirement of fast electronics and larger datasizes may make the technique impractical in terms of capital costs, availablespace near the detector, and computing power. To date the technique hasnot been deployed in an operating experiment. This work demonstrates thata cluster-counting drift chamber is a feasible option for an experiment suchas SuperB [55, 57]. SuperB was cancelled after the experiments describedin this paper, but the results are applicable to any drift chamber that isused for particle identification. The design of our prototype chambers wasstrongly influenced by the demands of SuperB , which are described in theTechnical Design Report [37].4.1.1 Drift ChambersDrift chambers are general-purpose detectors that can track and identifycharged particles [12, 63]. They consist of a large volume of gas with in-41strumented wires held at different voltages. When charged particles movethrough the chamber they ionize the gas particles. The electrons from theseprimary ionizations drift towards the wires held at high positive voltage,while the ions drift towards the grounded wires. The sense wires are verythin (∼ 20µm), such that the strong electric field accelerates the electronsenough to cause further ionization near the sense wire. The new electronsionize further into an avalanche, which is registered as an electronic signalon the sense wire. The amplification of the low-integer number of primaryionization electrons into a detectable signal on the wire is called the gasgain.The energy loss of a heavy (m & 1 MeV/c2) charged particle from pri-mary ionizations depends on its speed, as given by the Bethe formula [15]and various corrections [16]. The speed measurement is combined with theindependent momentum measurement from tracking, giving the particle’smass, which is a unique identifier. To measure speed, we measure or es-timate a quantity proportional to the number of primary ionizations. Atraditional drift chamber accomplishes this by measuring the total ioniza-tion per unit length of the track, which is proportional to the integral ofthe electronic signal on the sense wires belonging to a track. The theoret-ical probability distribution function for the total ionization is a Landaudistribution, which has an infinite mean and standard deviation [12]. Theconsequence is that if one takes the average of a number of samples (e.g. 40measurements of deposited charge in a track), the resulting distribution isnon-Gaussian and is dependent on the number of samples taken. Insteadof the mean of the distribution, one can use the most probable value forthe total ionization. This is accessed by a truncated mean technique. Ourtruncated mean procedure is described in Section Cluster CountingThe conventional technique described above is sensitive to gas gain fluctua-tions as well as the statistical fluctuations in the number of primary electronsproduced in each ionization event. Moreover, the truncated mean procedure42that is typically used discards a substantial fraction of the available informa-tion. None of these disadvantages exist if the number of primary ionizationscan be measured more directly.TechniqueThe cluster-counting technique involves resolving the cluster of avalanchingelectrons from each primary ionization event. This is done by digitizing thesignal from the sense wire in each cell and applying a suitable algorithm.The rise time of the signal from a cluster is approximately 2 ns, so electronicswith sufficiently high bandwidth are required.In principle, clusters can be detected as long as they do not overlap com-pletely in time. This can happen irrespective of the electronics involved dueto the probabilistic nature of the ionization process. Overlapping clustersare more likely for highly oblique tracks. Complex algorithms which con-sider signal pulse heights might disentangle even overlapping clusters, butthe algorithms tested in this work do not.An optimal algorithm would have a high efficiency for identifying trueclusters and a low rate of reporting false clusters (due to noise for example).PIDIn traditional drift chambers using the integrated signal, the signal ampli-tude is determined by the convolution of the probability of primary ion-ization, the number of primary electrons produced, and the variations ingas gain. This results in a long-tailed distribution that is typically dealtwith by the truncated mean procedure. Conversely, if clusters are perfectlyidentified, then the only variation is from the primary ionization, which isa Poisson process. No cluster counts need to be discarded to allow for aproper statistical treatment. In reality some counted clusters will be miss-ing or fake, the rate of these being caused by gas gain fluctuations, noiselevel, and the time separation capabilities of the electronics. The idea is thatthe sensitivity to these effects is small. The difficulty arises from the needto optimize a cluster-counting algorithm that may have many parameters.43A difficulty with both charge integration and cluster counting is the pres-ence of δ-rays [12]. These are electrons produced in primary ionizations thattravel far in the gas before further ionizing, such that they create their ownseparate ionization cluster. The production of δ-rays at a given momentumdepends only on the particle speed (∝ 1/β2) [16]. This inflates the chargeintegral and the cluster count with only a weak dependence on the speciesof the original particle, the result is a decreased PID resolution in general.The presence of δ-rays is one of the reasons why a truncated mean is usedin the charge integration method. While cluster counting is also affected byδ-rays, the effect is less pronounced, allowing all of the data to be used.Cluster TimingAny cluster-counting algorithm that uses a digitized signal is able to reportnot only the number of clusters in a cell, but also the arrival time of each ofthose clusters. In the oversimplified case of a linear and homogenous driftvelocity and infinite cells, the average spacing in time between consecutiveclusters would simply be proportional to the inverse of the number of clustersin the cell. In a more realistic scenario, the average spacing between clustersis useful information that is not one-to-one with the number of clusters.We can exploit the lack of perfect correlation and use the cluster timinginformation to further improve our ability to identify particles.TrackingFor tracking, cluster counting may also improve performance, but in a muchlesser degree and more subtle manner than as for PID. A traditional driftchamber uses only the arrival time of the overall signal in determining thedistance of closest approach from a sense wire. Unfortunately this arrivaltime measurement is vulnerable to noise, gas gain fluctuations (small initialclusters may be missed), etc. If the first few clusters are resolved, then whilethe first cluster arrival time is still the primary datum, the second clusterarrival time can be used as a consistency check. If the second cluster arrivesmuch too late, then the chance that the first cluster was a fake is greater, so44a smaller statistical weight can be assigned to that cell when reconstructingthe whole track. This paper deals only with the PID improvements and doesnot address tracking.4.2 ApparatusIn this section we describe the prototype drift chambers that were built, thecustom signal amplifiers and the various types of cables that were tested. Wealso describe the experimental setup in the test beam, the data acquisitionsystem, and the devices used for external PID and triggering.4.2.1 Prototype Drift ChambersWe built two nearly identical full-length (2.7 m) single-cell drift chambers,called chamber A and chamber B (Figure 4.1). The only difference betweenthe two chambers is the diameter of the sense wires: 20µm for Chamber Aand 25 or 30µm for Chamber B. More details about the wires are givenbelow.The wire layout creates a square cell 15 mm wide in a 10× 10 cm cross-section casing (for a gas volume of 2.7 × 104 cm3). Figure 4.2 shows a celldiagram including the dimensions and wire locations. The aluminium casingof the chambers has five large windows on two sides of the cell to allowparticles to enter and exit unimpeded. The windows are made of thin (∼20µm) aluminium, protected by aluminized Mylar.Different amplifiers are mounted on the endplates of the drift chambers,connected directly to the sense wires. The amplifiers vary in their gain,input impedance, and bandwidth. They are described in more detail inSection 4.2.2.We had the option of including a termination resistor to ground on thenon-instrumented side of the chamber. The required termination resistanceto prevent reflection of signals is 390 Ω. Runs were taken with and withouttermination, to see the effect of reflected signals on PID performance. Acircuit diagram showing our termination is in Figure 4.3.Runs were taken with chambers A and B strung with 20µm and 25µm45Chamber AChamber BabcdFigure 4.1: Photo of the prototype chambers mounted during ourbeam test. The far scintillator (Section 4.2.6) and additionalPMTs (Section 4.2.7) are visible in the background (labelled aand b respectively). The amplifier shielding boxes (c) are onthe right side of the picture. The smaller monitoring chamber(labelled d) (Section 4.2.8) is on top of Chamber B. The blue ar-row shows the path of the particle beam through our prototypesand two of the tungsten sense wires, respectively, and gold-plated aluminiumfield wires. For some later runs, chamber B was re-strung with a 30µmsense wire. The wires are connected to the endplates by the same crimp-pins and feedthroughs that were used in the BaBar drift chamber [38].The gas chosen for the test was a mixture of helium and isobutane ina 90 : 10 volume ratio. Helium was chosen because it reduces the effect ofmultiple scattering compared to the more typical argon [23]. Multiple scat-tering of the charged particles is the dominant contribution to the tracking46-1.8-1.6-1.4-1.2-1 -0.8-0.6-0.4-0.20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8-1.8-1.6-1.4-1.2-1-0.8-0.6-0.4- drift lines from a wirex-Axis [cm]y-Axis [cm]Gas: iC4H10 10%, 4He 90%, T=300 K, p=1 atm Isochron interval: 0.05 [µsec]Plotted at 08.55.31 on 27/03/13 with Garfield version 7.33.Figure 4.2: Garfield [4] simulation of isochrones for electron drifttimes in our prototypes, with 90 : 10 helium and isobutane.The isochrone intervals (dashed lines) are 50 ns. The full or-ange lines are the drift paths. The central point is the sensewire at high voltage, while the 8 points in a square around itare the field wires at ground. The extra 6 points outside the cellare bias wires to simulate the presence of an infinite network ofcells. The wire voltages are 1820 V and 1054 V for the sensewire and bias wires respectively.47HV10 kΩ 1.5 MΩSense Wire1000 pF390 ΩHV10 kΩ 1.5 MΩSense Wire1000 pFFigure 4.3: Circuit diagram representing the high voltage connectionto the sense wire with (top) and without (bottom) terminationresistor. Without the 390 Ω resistor, the signal can bounce.resolution at a B-factory like SuperB. In consideration of the rest of theSuperB detector, using helium reduces the number of radiation lengths rep-resented by the drift chamber. With isobutane as the quench gas, we areable to operate the chamber with a large helium fraction, further reducingthe amount of material. Helium also exhibits a lower drift velocity and ion-ization density, which also makes it an ideal choice for cluster counting asthe incoming clusters will be less likely to overlap in the digitized signal.The chambers are operated at room temperature and atmospheric pres-sure. We measured the temperature and pressure during the data takingperiods, we did not use these at any level of the analysis.4.2.2 AmplifiersWe used custom made amplifiers in order to achieve the bandwidth requiredfor cluster counting. The amplifiers are based on the AD8354 RF gain blockfrom Analog Devices. These have a reasonably low power consumption48(∼ 140 mW for the whole unit) and a bandwidth of 2.7 GHz. These deviceshave 50 Ω input and output impedance, and a fixed gain of 20 dB. The sim-plest configuration that we investigated was with two AD8354s in cascade.This provides very good bandwidth performance, but the input impedanceof 50 Ω creates a large mismatch with the characteristic impedance of thedrift chamber cells (around 370 Ω) and the signal to noise ratio is not op-timal. So, an emitter follower stage was added at the input, using a lownoise RF transistor (BFG425). This was configured either with 370 Ω inputimpedance, or with 180 Ω, as a compromise between impedance matchingand tolerance to stray capacitance. We also tried a configuration with anadditional low gain (2×) inverting stage (with a BFG425 transistor), having370 Ω input impedance. In this case, a single AD8354 gain block was used.The 370 Ω configuration gave the best overall results. A schematic of theamplifier setup is shown in Figure 4.4.In our final analysis, only the 50 Ω and 370 Ω amplifiers are considered.The data runs using the 180 Ω amplifiers gave signals which were of lowenough quality that a full analysis was not possible.4.2.3 Wire VoltagesThe correct voltage settings for the guard wires in the cell were determinedusing the computer program Garfield [4]. The guard wire voltages are chosento make the sensitive region of our cell behave as if it were part of an infinitearray of identical cells. These voltages scale linearly with the chosen sensewire voltage.The sense wire voltages were tuned to obtain roughly equal-amplitudepulses for all combinations of chamber and amplifier. This was done empir-ically by looking at the fraction of events on the oscilloscope (Section 4.2.8)that saturated the full voltage range. The voltage was tuned until this frac-tion was ∼ 15 %.The resulting voltage for chamber A (20µm sense wire) using one of the50 Ω amplifiers is 1700 V. The corresponding electric field at the wire surfaceis calculated by Garfield to be 217 kV/cm.49Preamplifiers;	  simplified	  diagram	  Two	  cascaded	  RF	  gain	  blocks	  Z=	  50	  ohms	  Total	  gain	  =	  40	  dB	  Analog	  Devices	  AD8364	  27K	   150Ω	  15Ω	  1µf	  1µf	  1.8nf	  3	  KV	  Detector	  wire	   Out	  D1	  D2	  D3	   D4	  +4V	  BFG425	  OpSonal	  front-­‐end	  (FE)	  c	  e	  R	  C	  L	  	  Preamplifier	  type	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  FE	  	  	  	  	  	  	  	  	  	  	  	  	  R	  	  	  	  	  	  	  	  	  	  	  	  L	  	  	  	  	  	  	  	  C	  posiSon	  	  50	  Ω	  direct	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  not	  used	  	  	  	  	  	  -­‐-­‐-­‐-­‐	  	  	  	  	  	  	  	  	  -­‐-­‐-­‐-­‐	  	  	  	  	  	  	  	  	  	  -­‐-­‐-­‐-­‐	  	  180Ω,	  non	  inverSng	  	  	  	  	  	  	  	  	  	  	  used	  	  	  	  	  	  	  	  	  180	  Ω	  	  	  15nHy	  	  	  	  	  	  e	  	  370Ω,	  non	  inverSng	  	  	  	  	  	  	  	  	  	  	  used	  	  	  	  	  	  	  	  	  370	  Ω	  	  	  68nHy	  	  	  	  	  	  e	  	  370Ω,	  	  	  	  	  	  	  	  	  inverSng	  	  	  	  	  	  	  	  	  	  	  used	  	  	  	  	  	  	  	  	  370	  Ω	  	  	  68nHy	  	  	  	  	  	  c	  Figure 4.4: Simplified schematic of the amplifiers used in the experi-ment.4.2.4 CablingFor some of the runs we varied the type of signal cable used to connect theoutput of the amplifiers to the data acquisition system. We used two dif-ferent types of Sub-Miniature RG-59/U cables (models 1855A and 179DTfrom Belden) and Miniature Coax (model 1282 from Belden), all with 75 Ωimpedance. The lengths were all 10 m, which is the distance between the am-plifiers and digitizers for SuperB. From the signal-propagation perspective,the 1855A is a better cable than the 179DT, having less signal attenuation(34 db/100m versus 70 dB/100m at 1 GHz). From the perspective of me-chanical integration with the rest of the detector however, the 179DT cablewould be preferable to the 1855A, being lighter, thinner, and allowing asmaller minimum bend radius (25.4 mm versus 38.1 mm).We also took data with a header connector between the amplifier and thesignal cable to simulate a connector through the real drift chamber bulkhead.The header connector has 20 pins with a 2.54 mm pin spacing. Only two50LeadCollimatorNear TOFScintillatorChamber A Chamber BHigh Voltage EndAmplifier EndAdditionalTriggerScintillatorFar TOFScintillatorBeam PipeExitBeamDirectionFigure 4.5: Schematic of beam test setup at the TRIUMF M11 facil-ity. The distances in this schematic are not to scale, though thedrift chamber proportions are correct.pins are used in the connector to connect the ground and signal parts of anadditional 30 cm 1855A cable which is inserted in our signal cable lengthusing regular BNC connectors.4.2.5 Test BeamData were collected at the TRIUMF M11 beam [64], which simultaneouslydelivers positrons, positive muons, positive pions at a tuneable momentumrange of 100 to 350 MeV/c. We block residual protons from upstream usinga slab of polypropylene at the mouth of the beam pipe (6.35 mm thick at210 MeV/c). We can determine the beam populations using the time-of-flight system described in Section 4.2.6.The prototypes were mounted on a rotating and moveable table, whichallowed us to take runs at different dip angles and positions along the lengthof the sense wires. A schematic of the beam test setup is in Figure 4.5 anda photo of the test hall is in Figure 4.1.51Most of the data were collected at 210 MeV/c, a relatively low momen-tum for a high-energy particle physics experiment. At this momentum how-ever the Bethe formula separation of pions and muons is similar to theseparation of pions and kaons at 2 GeV/c. This is confirmed by our simula-tions at both momenta, described in Section 4.3. High-efficiency separationof pions and kaons at 2 GeV/c is critical for high-precision measurementsand reconstructions at a high-energy particle experiment like SuperB.4.2.6 Time of FlightAn external time of flight (TOF) system was used to identify the particlesindependently of the prototypes. The beam’s momentum spread is smallenough that a histogram of the TOF shows distinct peaks corresponding tothe species of the particles in the beam. The TOF system consists of twocounters ∼ 4 m apart, one upstream of the prototypes and one downstream(Figure 4.5). The counters are 12.7×12.7×220 mm BC-404 scintillators eachread out by two Burle 8501-1 64-channel micro-channel plates (MCPs), oneon each end of the scintillator block. The scintillators are roughly the samesize as the beam spot. The MCPs have 25µm pores. Each of the 64 channelsin the MCPs have an active region of 6 × 6 mm. We gang together four ofthe channels to form one combined signal. This signal from each MCP goesto an Ortec 935 constant-fraction discriminator (CFD) with no pulse heightcorrection applied. Each is then delayed by a given time in order to separatethe pulses, then they are combined and recorded in a single channel of ouroscilloscope.The signals from the MCPs are used as part of the trigger. Addi-tional signals from photomultiplier tubes are used and are described in Sec-tion 4.2.7.The unscaled TOF is obtained by determining the arrival time of eachpulse from the MCPs as recorded by the oscilloscope. The first two pulsesare from the two ends of the upstream counter, while the following two arefrom the downstream counter. These pairs are averaged, then the differenceis taken. There are arbitrary delays associated with the MCP signals, so52Time of Flight (ns)13 14 15 16 17Counts/0.05ns0200400600800100012001400160018002000e+ µ+ pi+Figure 4.6: Time-of-flight histogram for a run at 210 MeV/c beammomentum. The three peaks correspond to positrons, muons,and pions, in increasing TOF order. The fit is to the sum ofthree Gaussian distributions.the TOF quantity is scaled to be physically meaningful. A run is chosenand a histogram of the TOF quantity is made, where the positrons, muons,and pions are clearly resolved as Gaussian peaks. We fit the positron peakwith a Gaussian distribution. The beam momentum is high enough thatthe positrons may be treated as moving at the speed of light, and the actualdistance between the two counters is well-measured.We were able to achieve TOF resolutions of ∼ 60 ps per MCP. For a210 MeV/c beam (Figure 4.6) the separations of the Gaussian peaks aregreater than the 3σ ranges used to identify particles in our track compositionprocess described in Section 4.5.2. A sample trace of the actual TOF signalis shown in Figure 4.7, where the first four pulses are from the MCPs.We fit the TOF distribution with the sum of three Gaussians and counthow many particles are within 3σ of each peak. For the run shown in53Figure 4.6, we find that of all the physical triggers 3.8% are positrons, 20.5%are muons, and 75.7% are pions.4.2.7 TriggerThe TOF signals are also used as part of the trigger system for the oscillo-scope. It was noted that with only the upstream and downstream counters,many events contained no signals in the drift chambers (i.e. oscilloscopetraces with just normal noise, no clusters). In addition, the TOF histogramshowed six peaks, though only three were expected. The six peaks appearedto be in two similar groups, shifted in TOF value. The conjectured originof the higher-TOF valued population was beam particles passing throughthe upstream counter but angled downwards, scattering off of the metal ta-ble, then passing through the downstream counter, bypassing the chambersentirely and taking a longer path.A third scintillator strip 3 mm thick was placed between the prototypesand the downstream counter (Figure 4.5), instrumented with photomulti-plier tubes. The coincidence of the three (upstream, downstream, strip)was required for a physical trigger. This additional requirement removedthe extraneous TOF population and many of the events with no drift cham-ber signals. Part of the trigger signal can be seen in Figure 4.7 in the uppertrace. The third scintillator was not digitized and thus is not visible in thefigure.The coincidence rate is ∼ 30 Hz, while the signal rate on the upstreamcounter without requiring coincidences ranges from a few kHz to tens ofkHz, depending on beam line settings. We also introduced an asynchronoustrigger based on a pulse generator whose frequency was tuned to ∼ 15% ofthe total trigger rate. These asynchronous triggers are uncorrelated withreal beam events. They provide a sample of empty events for monitoringand measuring baseline voltages and noise levels during the run.54Figure 4.7: Oscilloscope traces for a run at 210 MeV/c beam momen-tum. The first is the TOF signal, with four initial pulses fromthe TOF MCPs, and two additional pulses from the extra trig-ger PMT. The TOF value identifies this particle as a pion. Thesecond and third traces are from prototypes A and B, respec-tively. The cluster structure is clearly evident in these signals.4.2.8 Data Acquisition SystemOur data acquisition system consisted of a LeCroy WavePro 740Zi, an oscil-loscope with 4GHz bandwidth. Data were written to an external USB harddisk in a proprietary binary format and then converted into ROOT [3] filesfor analysis. The oscilloscope writes one file per active channel per trigger.We used one channel for the time-of-flight system and one channel for eachprototype sense wire, meaning we had three small files written per trigger.Each channel read 20002 samples with 50 ps spacing, for a trace duration of55∼ 1µs. The biggest bottleneck was the filesystem (Microsoft NTFS), whichdoes not perform well with directories having tens of thousands of files. Theoverall rate of events written to disk was ∼ 12 Hz.We used the MIDAS [65] data acquisition system to automatically recordtemperature and atmospheric pressure as well as the current in a small mon-itoring chamber. The monitoring chamber was connected in series with theprimary chambers on the gas line, and was exposed to an 55Fe source. Themonitoring chamber wire voltages were held fixed, allowing us to monitorthe gas and environmental conditions by tracking changes in the gas gain.4.3 SimulationsWe used a gaseous ionization detector simulation package called Garfield [4]to simulate tracks through our prototypes. We did not simulate the electron-ics chain and the data acquisition system, but we are able to get predictedcharge depositions and cluster counts for our specific gas mixture and wireconfiguration.The charge deposition is not reported directly, but is proportional to theenergy lost by charged particles passing through the gas. It is plotted inFigure 4.8 for muons, pions, and kaons. The momentum scale is chosen toillustrate the fact that the difference in energy loss between pions and muonsat ∼ 200 MeV/c is similar to that between pions and kaons at ∼ 2 GeV/c(Section 4.2.5).The number of primary ionizations is reported directly by the simulationsoftware and can be treated as a “true” number of clusters. It does notdepend on the choice of electronics, algorithms, and it does not count δ-rays(Section 4.1.2). The distribution of primary ionizations for muons, pionsand kaons is shown in Figure 4.9 and also shows the similarity betweenmuon-pion separation at our beam momentum and pion-kaon separation athigher momenta. It is also important to point out that the absolute numberof clusters for muons and pions at 210 MeV/c approximately mirrors that ofpions and kaons at 2 GeV/c, not just the difference. The absolute value isimportant because it is related to our ability to actually resolve the clusters.56Momentum (MeV/c)100 1000dE/dx (keV/cm) +µ+pi+KFigure 4.8: Garfield simulation of the energy loss by a charged particlecrossing 40 cells of a 90:10 mixture of helium and isobutane. Theblack squares, red circles, and green triangles represent muons,pions, and kaons, respectively. The marker position is the 70 %truncated mean energy loss, while the vertical error bar on eachmarker is the RMS of the truncated mean.4.4 Beam Test DataThe data were taken during August and September 2012. Approximately200 runs of 30000 events were acquired. A run is a contiguous data-collectionperiod during which no setup parameters are changed. On average, 15 % ofthe events were from asynchronous triggers and 10 % of the physical triggersdid not leave signals in the prototypes.Various parameters were changed from run to run. These were: thesense wire voltages, amplifiers, signal cable types, beam momentum, angleof incidence of the beam with the chamber, beam position along the sensewire length and presence of a proper termination resistor on the sense wire.57Momentum (MeV/c)100 1000clusters/cm    1015202530 +µ+pi+KFigure 4.9: Garfield simulation of charge clusters produced by acharged particle crossing a 90:10 mixture of helium and isobu-tane. The black squares, red circles, and green triangles repre-sent muons, pions, and kaons, respectively. The marker positionis the average number of clusters, while the vertical error baron each marker is the RMS.In the end, many runs turned out to be recorded using unsuccessful amplifierprototypes and could not be used for a detailed analysis. This analysis uses20 runs, for a total of 633050 recorded events.4.5 AnalysisThe analysis of the test-beam data is performed in two steps, both of whichare done offline (after the data for that run has been fully collected). Thefirst step involves analyzing the signals (voltage as a function of time) fromthe three oscilloscope channels. The first channel is connected to the time-of-58flight (TOF) system, with voltage pulses corresponding to a particle crossingthe scintillators before and after the drift chambers. The second and thirdoscilloscope channels are connected to the amplifiers on the sense wires ofthe two drift chambers.The second step of analysis involves constructing multi-cell “tracks”from the single-cell events using a composition process (described in Sec-tion 4.5.2). Single-cell events are taken from the same run, same chamber,and having a TOF consistent with the same particle type. Forty of theseare used to build up a track as if it were traversing a full SuperB -size driftchamber.4.5.1 Single-Cell InformationThis section describes in detail the first stage of analysis in which we dealwith single-cell events. The time-of-flight is measured, the signal is adjustedfor baseline drift and basic quality controls are imposed. In this stage wealso perform the charge integration and use cluster-counting algorithms tocount clusters on the drift chamber signals.Time of FlightThe time-of-flight is determined by applying a simple threshold-over-baselinealgorithm to the oscilloscope trace from the channel connected to our scin-tillator MCPs and PMTs. A valid TOF signal consists of four identifiedpulses, while an asynchronous trigger has zero pulses. Events with one, two,or three TOF pulses are rejected, and represent the small fraction of eventsfrom asynchronous triggers with a pulse in one of the TOF counters.Baselining and Signal ConfirmationThe baseline voltage for each drift chamber is simply the average voltage ofthe entire signal from the previous asynchronous trigger. The RMS deviationfrom this baseline is also measured. The mean of these RMS deviations is∼ 2 mV. Signals from physical triggers have amplitudes on the order ofhundreds of mV above the baseline.59The real particle events are tested for the presence of an actual signal by athreshold algorithm, where the baseline and threshold levels are determinedby the previous asynchronous trigger measurements. Real particle eventsthat have no signal in the chambers are rejected. These are from eventswhere a real particle crossed the scintillators, but either missed one or bothdrift chambers, or did not interact within them.Charge IntegrationA charge integration is performed for the remaining asynchronous and phys-ical events, starting at the time of the threshold crossing mentioned in Sec-tion 4.5.1 (or at an arbitrarily chosen time for asynchronous events), inte-grating for a fixed duration. The distribution of start times for a samplerun is shown in Figure 4.10. If the duration is too short, then some pulsesmay be missing or the tail of the last pulse may be clipped. If the durationis too long, then unnecessary noise is also integrated, reducing the resolvingpower of the charge measurement. Different equipment combinations givedifferent pulse tail decay times, so the duration must be optimized empir-ically. A typical optimal value is ∼ 600 ns, as shown in Figure 4.11. Theoptimization of the integration time is described in Section 4.6.1.From the integrated charge we subtract a pedestal calculated from theprevious asynchronous trigger. This pedestal is a charge integration withthe same integration time, but a fixed starting time. The result is a baseline-subtracted charge, which should have a smaller systematic error than the rawcharge integral. The distribution of integrated charges for physical triggersand asynchronous triggers is shown in Figure 4.12. The physical triggers areshown separately for each species in Figure 4.13.Cluster CountingCluster-counting algorithms can vary in complexity, efficiency, and in theirrate of reporting fake clusters. Here we briefly describe the various algo-rithms, but precise definitions can be found in Section 4.8.The algorithms involve two forms of smoothing of the oscilloscope traces60ns0 100 200 300 400 500 600 700 800 900 1000Counts/10.0 ns02004006008001000Figure 4.10: Time at which the charge integration begins in ChamberA for a run at 210 MeV/c.(Figure 4.14). The first is a “boxcar smoothing” where each sample is re-placed with the average of itself and the n−1 previous samples. The secondis a true averaging procedure, where the number of points in a trace isreduced and each point is the average of n points.All of the algorithms involve some kind of transformation of the smoothedsignal, and a threshold-crossing criterion. The transformed signals for thevarious algorithms are shown in Figure 4.15. One of the most basic cluster-counting algorithms is the “Threshold above Average”. It subtracts thenon-smoothed signal at time t from the boxcar-smoothed signal at timet− 1, then applies a threshold.A more general algorithm (of which the previous is a special case) isthe “Smooth and Delay” algorithm. It involves smoothing two copies of thesignal by different amounts, delaying one of the copies by a certain number offrames, then taking the difference and applying a threshold. This algorithmhas four parameters, and is thus more difficult to optimize.61ns0 200 400 600 800 1000V0.40.420.440.460.480.5Figure 4.11: Sample event in chamber A showing 600 ns integrationtime.The two algorithms above essentially implement a first-derivative method.We also implemented a second-derivative method. This one uses the trueaveraging procedure rather than the “boxcar smoothing”. The first deriva-tive is first calculated by taking the difference between consecutive smoothedsamples. The second derivative is then calculated by taking the differencebetween consecutive first derivative values. Each time, we divide by the timeinterval represented by a sample, to keep the units consistent. The numberof clusters counted using the second derivative is shown for each particlespecies in Figure 4.16.All of the threshold algorithms in principle trigger on the leading edge ofcluster signals. However it is noticeable that real cluster pulses have a verysharp leading edge (approximately 3 ns) and a slower decaying trailing edge(approximately 100 ns). Fake clusters are more symmetric, returning to thebaseline voltage faster than the signal from a real cluster. Thus an algorithmwas devised that takes cluster candidates from the above algorithms, but62pC0 100 200 300 400 500 600Counts/(2.0 pC)020040060080010001200Beam TriggersAsynchronous TriggersFigure 4.12: Baseline-subtracted charge distributions as identified bythe time-of-flight system. The sharp peak on the left is fromasynchronous triggers (with no particles in the prototypes),while the broader peak in the middle is from physical triggerswith all particle species combined.requires the pulse to last a minimum duration in order to be confirmed.Pulses that return to baseline too quickly are discarded as fake clusters.This “timeout booster” allows the use of smaller thresholds, which whileincreasing the efficiency of finding real clusters also admits more fakes. Thetimeout criterion removes most of the fakes but keeps the real clusters.As mentioned before, each of the cluster-counting algorithms can returnnot only the number of clusters, but the actual time at which each clusterwas found. We investigated the use of this information, in the form of anaverage time separation between clusters in each cell.63PositronEntries  650Mean    257.1RMS     99.41-100 0 100 200 300 400 500 600Counts/7.0pC0510152025pCMuonEntries  3501Mean    208.6RMS     99.62-100 0 100 200 300 400 500 600Counts/7.0pC020406080100120140pCPionEntries  12957Mean    225.4RMS     100.1-100 0 100 200 300 400 500 600Counts/7.0pC0100200300400pCFigure 4.13: Baseline-subtracted charge distributions for each parti-cle species at 210 MeV/c. Note that the sample mean andRMS values indicated in the figure are not representative ofthe underlying distribution since it does not have well-definedmoments.4.5.2 Track CompositionThe prototypes have only a single cell. The traditional method of identifyingparticles using the truncated mean requires many cells forming a track. Thuswe construct tracks from the single-cell events.To compose a track for a given species of particle, we select (with replace-ment) random single-cell events that have been identified with the time-of-flight information. We positively identify particles with TOF values within3 standard deviations of the central values of the three Gaussian peaks cor-responding to the particle species. For a typical run with e.g. 3500 singlemuon events, the number of possible muon tracks is astronomical (∼ 1094),and the likelihood of a given track being composed of multiple copies ofthe same single-cell event is low (∼ 1%). We also form empty tracks by64ns0 200 400 600 800 1000V0.340.360.380.40.420.440.460.480.5Boxcar  ns0 200 400 600 800 1000V0.340.360.380.40.420.440.460.480.5AveragingFigure 4.14: The two smoothing algorithms used, each smoothingover 125 frames of 50 ps width, for a smoothing width of6.25 ns. This event is the same as shown in Figure 4.11combining the signals from asynchronous events.The information from each event is combined to form the track informa-tion. The track information is the particle species, total number of clustersfound per cm of track, and the truncated mean of the charge integrals fromeach cell. The truncated mean is performed by sorting the list of chargeintegrals and taking 70 % of the values starting from the beginning of thelist. The value of 70 % was roughly optimized to give better separation, forcomparison 80 % was used in BaBar [38]. The SuperB drift chamber designhas 40 layers. Thus we use 40 events from our single-cell prototypes eventsto create a composed track. The 70 % truncated mean was thus done byrejecting the largest 12 integrated charge values from the cells.In the case of tracks formed from asynchronous events, the list is notsorted, since these values are already Gaussian, but still the same fraction of65Figure 4.15: Illustration of the quantity on which a threshold is ap-plied in the various cluster-counting algorithms. Each uses aset of parameters (smoothing width, threshold level) that wereoptimized for this run. The threshold level is indicated by thered horizontal line. The last image is the same as the secondderivative, but with the binning shifted, to show that someclusters can be hidden by the binning (e.g. around 480 ns).This event is the same as shown in Figures 4.11 and 4.14values is discarded. The distribution of truncated mean charge and clustersfor the composed tracks is shown in Figures 4.17 4.18, respectively.We also form the track-wise average time separation between clusters bydoing a weighed average of the cell-wise average cluster separation for theevents in the track. The weights are the number of clusters in the cells.It is worth noting that the relative separations of the muon and pionpeaks shown in Figures 4.17 and 4.18 are very different. For the truncated66PositronEntries  650Mean    15.05RMS     3.0775 10 15 20 25 30 35Counts/1.0 clusters020406080ClustersMuonEntries  3501Mean    13.65RMS     3.1575 10 15 20 25 30 35Counts/1.0 clusters0100200300400ClustersPionEntries  12957Mean    14.27RMS     3.1095 10 15 20 25 30 35Counts/1.0 clusters050010001500ClustersFigure 4.16: Number of clusters found for each species as identifiedby the TOF system. This is for a 210 MeV/c run using thesecond-derivative algorithm.mean of the integrated charges, the relative separation between the peaks(difference in the location of the peaks, divided by the average of the two) is∼ 10 %, while for the cluster counting it is ∼ 5 %. Na¨ıvely this should meanthat the cluster counting technique is less effective. However because thewidths of these peaks are also very different, the two techniques turn out tobe of comparable power (Figure 4.19).4.5.3 Combined Likelihood RatioIn order to combine the information from the truncated mean and the clustercount, we form likelihoods based on fits to the two quantities. These quan-tities are reasonably Gaussian (for non-empty tracks), so we fit them withGaussian distributions Gs,k, for particle species s and measured quantity k.For a given track, the likelihood of the track coming from a particle s is67pC/cm60 70 80 90 100 110 120 130Counts/(1.0 pC/cm)0200400600800100012001400160018002000 +eµpiµ+pi+e+Figure 4.17: Truncated mean of charges (dE/dx) in composed tracks.This is using events from the same run as Figure 4.13. Thethree peaks from left to right are from muons, pions, andpositrons, respectively. Here the particle populations areequal, as we compose an equal number of tracks for eachspecies.found by evaluating the product of the fitted distribution functions for bothks at the measured values. Thus if the measured truncated mean charge fora track is q and the clusters per cm of track are n, the combined likelihoodisLs(q, n) = Gs,charge(q)×Gs,clusters(n). (4.1)This combined likelihood ignores any correlation between the two quanti-ties. The correlation is indeed non-zero but is somewhat weak (∼ 0.3). Pos-sibly combined likelihood models which make use of the correlation wouldbe more effective, but we did not investigate this.As mentioned in Section 4.2.5, the ability to identify muons and pions at68Clusters/cm7.5 8 8.5 9 9.5 10 10.5Counts/(Clusters/60 cm)0100200300400500600+eµpiµ+ pi+ e+Figure 4.18: Number of clusters per cm in composed tracks. This isusing events from the same run as Figure 4.16 and using thesecond-derivative algorithm. The three peaks from left to rightare from muons, pions, and positrons, respectively. Here theparticle populations are equal, as we compose an equal numberof tracks for each species.∼ 210 MeV/c is our proxy variable for the performance of the prototypes.Thus we form a ratio of the combined likelihoods of being a muon and pion:R(q, n) =Lµ(q, n)Lµ(q, n) + Lpi(q, n). (4.2)This quantity’s distribution is peaked at 0 for real pions and at 1 forreal muons. A cut can be made that maximizes the separation accordingto some figure of merit. A typical way to demonstrate the performance isby making a rejection-selection efficiency plot. Consider the fraction of realpions that would also be identified as pions by the cut on R, and the fractionof real muons that would not be identified (that is, rejected) as pions by thecut on R. We can thus make a parametric plot of muon rejection efficiency69Pion Selection Efficiency0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Muon Rejection Efficiency00. onlyCluster counting onlyCluster timing onlydE/dx and clusters countingdE/dx, clusters counting and timingFigure 4.19: Efficiency graph for a run at 210 MeV/c, the same run asearlier figures. The cluster counting is done using the second-derivative algorithm. The upper two curves nearly coincideand are the efficiencies when cutting on the combined likeli-hood ratios. One combines the truncated mean, cluster count,and cluster separation, the other only truncated mean andcluster count. The lower three curves are the efficiencies whenone cuts directly on the truncated mean, cluster count, or clus-ter separation quantities.on the vertical axis and pion selection efficiency on the horizontal axis, withthe parameter being the chosen R cut value (Figure 4.19). Similar efficiencygraphs can be made for cuts directly on the physical quantities of chargeand cluster counts.4.5.4 Figures of MeritThe efficiency graphs are a good way to represent the performance of aparticular setup, but they are two-dimensional and difficult to include insummaries. Thus we construct figures of merit in order to quantify the70performance of an equipment choice or algorithm. A convenient method isto set a given background rejection level and state the corresponding sig-nal efficiency. In the muon rejection and pion selection plot, one may thusfind the muon rejection efficiency corresponding to 90 % pion selection effi-ciency, or vice-versa. These figures of merit are easy to interpret physicallyand correspond to how detector performance is typically quantified in pastexperiments.An alternative figure of merit turns out to better differentiate betweenalgorithm parameter choices, but has a much less intuitive physical meaning.It is the maximum excursion on the muon rejection and pion efficiency plotfrom the origin of the graph. The curves on the graph approach (0, 1) and(1, 0) in the limits of R cut values of 0 and 1 respectively, but the curvescan lie above that inscribed by a circle of unit radius. The length of thelongest straight line joining (0, 0) and the efficiency curve is taken as thefigure of merit. In certain cases the performance is bad enough that thelines lie below that inscribed by a circle, in this case the alternative figureof merit is not meaningful, as it is identically 1.All three figures of merit can be shown to be equivalent, in the sensethat local maxima and minima lie in the same regions of parameter space.The maximum-excursion-from-origin figure gives better separation for thoseruns where it is meaningful (the majority). It is used for the optimizationof algorithms, but the results are presented using the more intuitive figureof merit of pion selection efficiency at 90 % muon rejection.4.6 ResultsIn this section we present the results of varying the cluster-counting algo-rithms, gas gain, various chamber positions, and other equipment choices.4.6.1 Charge IntegrationThe time over which to integrate a signal in order to capture the chargedeposition on the wire was determined empirically. In principle the optimalvalue varies from run to run depending on gas gain, dip angle of the beam,71Integration Time (ns)100 200 300 400 500 600 700Pion Selection Efficiency00. RunWindow Near AmplifierHalf GainLow MomentumFigure 4.20: Pion selection efficiency using dE/dx only for severalruns as a function of charge integration time. The baselinerun is at a window 1883 mm from the amplifier, 210 MeV/cand using nominal gain as calculated by simulations. The low-momentum run is at 140 MeV/c. All the runs use the extratermination resistor.and window position, but we wish to compare runs at different settings.Thus we look at the figure of merit for many different runs and choose asuitable compromise (Figure 4.20). As it turns out, the performance doesnot vary strongly as a function of integration time once the time is suitablylong. We choose an integration time of 600 ns for the rest of the study.4.6.2 Cluster CountingThe various cluster-counting algorithms have parameters that must be tunedempirically. By iterating this procedure many times using the same run, a“map” of the figure of merit can be created in the algorithm parameter space,the maxima of which are optimal values for the algorithms (Figure 4.21).72Averaging Window (ns)3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5)2Threshold (mV/ns-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10-310×0.460.480.50.520.540.560.580.60.62Figure 4.21: Example performance “heat map” for the second-derivative algorithm using a run at 210 MeV/c. In this case,the optimal parameters are an averaging window of ∼ 6.5 nsand a threshold of ∼ −0.16 mV. The black rectangles are thehighest-performance regions, the magenta is the single best.The colour scale refers to the optimized figure-of-merit fromSection 4.5.4.While the figure of merit includes the PID performance from dE/dx andcluster counting, the dE/dx contribution is essentially constant even withthe randomness introduced by the track composition process.The optimal parameters vary from algorithm to algorithm and depend onthe run used to optimize the parameters. In an operational experiment, onlyone set of parameters can be chosen, so some compromise will be necessary.Nevertheless, to compare the algorithms themselves, we may compare theperformance of each algorithm when optimized on the same data run.The chosen run has the following parameters: 10 degree dip angle, win-dow 1883 mm from the amplifier, and 20µm sense wire. A 370 Ω inverting73amplifier and 1855A Sub-miniature RG59/U signal cable with no extra con-nector are used. The beam momentum was 210 MeV/c. A total of 30784triggers were recorded of which 7720 are asynchronous, and 680, 3649, and13579 are positively identified as positrons, muons, and pions respectively.The remainder have TOF values more than 3σ away from the peaks or haveno signal in the chamber.The dip angle of 10 degrees was chosen rather than 0 in order to avoidspace charge effects. The avalanches produced on the wire from the passageof a particle at zero degrees occur all in the same gas volume near thewire. This can affect the overall results and essentially makes 0 degrees a“special” angle. In an operating e+e− collider experiment the fraction oftracks suffering from space charge effects is negligible.We explored a variety of algorithms, which are described in detail inSection 4.8. Each has some kind of threshold as one of the parameters,and some smoothing or averaging duration. A common feature is that theoptimal smoothing or averaging duration is ∼ 5 ns, which indicates thatextremely high sampling rate and bandwidth are not necessary to improvePID with cluster counting. The smoothing times correspond to Nyquistfrequencies of ∼ 100 MHz. Our amplifiers have much higher bandwidththan this (Section 4.2.2), so using amplifiers with smaller bandwidth butbetter signal-to-noise ratios should improve overall performance.In Table 4.1, the figure of merit is the pion selection efficiency for 90 %muon rejection. Here and in later plots, it is difficult to give a good estimateof the systematic uncertainty as many factors were not taken into account.For example the temperature of the gas in the chamber plays no role inour calculations, though the temperature did change during the data takingperiod. The track composition process involves drawing random numbers, soa contribution to the uncertainty from this can be estimated by composingmultiple sets of tracks and seeing the distribution of results. Running thecode 100 times yields an RMS deviation from the mean of ∼ 0.05. The meanis what is reported in Table 4.1.In the table, only algorithm C uses the “Timeout Booster” technique.We also tried applying the technique to the other algorithms, but it was no-74Table 4.1: Summary of optimal parameters for the various cluster-counting algorithms. The algorithms labelled A, B, C, D, andE are “Signal above Average”, “Smooth and Delay”, “Signalabove Average with Timeout”, “Second Derivative”, and “Sec-ond Derivative (Two Passes)”, respectively. The threshold isgiven with the appropriate units for that algorithm, and τ is thesmoothing or averaging time in nanoseconds. Algorithm B hasin principle two smoothing times, but the optimal value has themequal. The additional parameter ∆t for the algorithms B and Care the delay and the timeout, respectively. The figure of meritpi is the pion selection efficiency for 90 % muon rejection.Algorithm Threshold τ(ns) ∆t(ns) piA -6.5 mV 3.5 0.62B -0.1 mV 2.75 3.75 0.64C -3.0 mV 3.5 4.25 0.62D 0.16 mV/ns2 6.5 0.64E 0.15 mV/ns2 6.25 0.64ticed that if the algorithm already has reasonable performance, the improve-ment from the timeout is negligible. Indeed the optimal timeout duration forthe “Smooth and Delay” algorithm is zero, yielding the same performanceas the bare algorithm.Overall the best algorithm is the two-pass second derivative algorithm,but it is only marginally better than the other algorithms. The difference isless than the typical variation due to the track composition process.It is fortuitous that even the simple algorithms have good performance,as they are reasonable to implement using a field-programmable gate array(FPGA) or even analog hardware.In some sections that follow, the PID performance with optimized clustercounting refers to the use of a cluster-counting algorithm where the param-eters were chosen to give the best figure of merit for that run. The optimalparameters vary from run to run, so in each case, we also run the algo-rithm on a given run using parameters that were optimal for a set of otherruns. The other runs each vary in only a single parameter: the window,the HV settings, and the momentum. The average performance using these75Cluster Separation (ns)50 55 60 65 70Counts/0.2 ns020040060080010001200+eµpie+pi+µ+Figure 4.22: Track-wise weighed average of time intervals betweenclusters, in 50 ps units for each particle species. This is a runat 210 MeV/c. The three peaks from left to right are frompositrons, pions, and muons, respectivelynon-optimal parameters is labelled “sub-optimal cluster counting” in laterfigures.4.6.3 Cluster Timing for PIDIn each cell, we take the average of the time intervals between consecutiveclusters. In the track composition process, we form a weighted average ofthe cell-wise averages, with the weights given by the number of clusters ineach track. The resulting quantity gives a reasonable separation for eachparticle type (Figure 4.22).Unfortunately the performance is not as good as either the traditionalcharge integration or cluster counting (Figure 4.19). In addition, if we forma tripartite combined likelihood, the improvement relative to the bipartitecharge integration and cluster counting combination is negligible. Given the76increased computational complexity of calculating the average separations,it is unlikely that the timing information will be useful for PID purposes ina real particle physics experiment.4.6.4 Dependence of PID on Gas GainThe gas gain of the prototypes depends on the choice of sense wire voltageand on the gas. We tested only one gas, a mixture of helium and isobutanein a ratio of 90 : 10. A nominal voltage was selected as described in Sec-tion 4.2.3. The actual gas gain for our gas mix and voltages is on the orderof 105, measured offline using an 55Fe source. The procedure aims to obtainoscilloscope signals with roughly the same amplitude with all the amplifiers.The dependence of gas gain on sense wire voltage is approximately exponen-tial [66]. In our case a ±60 V change corresponds to a doubling or halvingof the gas gain. The resulting performance after doubling and halving thegain is shown in Figure 4.23.Previous to the experiment, the intuitive notion was that higher gasgains would be better, since the signals would stand out more from therandom noise on the chamber wires. It appears however that this is not thecase and that indeed better PID performance can be obtained at lower gasgains. Lower performance at higher gas gains is either due to gas effects ( charge) or to the amplifiers. We did not explore the even lower gainswhere the performance is expected to decrease again. Data runs using otheramplifiers with different gain do show the eventual decrease (Section 4.6.7),so the optimal voltage is not too far from that shown in Figure 4.23 (within∼ 100 V).When choosing a gas gain for an experiment the most important featuresare more often the tracking performance, ageing issues, and operationalissues. This is more likely to influence the choice of specific gain, regardlessof the PID performance. However, if PID performance is also highly valued,lower gains should be explored.77Gas Gain (Arbitrary Units)0.6 0.8 1 1.2 1.4 1.6 1.8 2Pion Selection Efficiency00. OnlyWith Optimized Cluster CountingWith Suboptimal Cluster CountingFigure 4.23: Variation in PID performance at the three gas gains thatwere explored. This is a run at 210 MeV/c using an inverting370 Ω amplifier.4.6.5 MomentumAs shown in Figure 4.24, the difference of ionization between pions andmuons is greater at lower momenta. This is in agreement with theoreticalexpectations and simulations. As expected, the improvement from addingcluster counting is most noticeable at the momentum where the overall per-formance is worst, making the detector response more uniform.4.6.6 Dependence of PID on Window (Z-position)The prototypes have five windows at five thin aluminium positions alongtheir 2.7 m length. The reference point is chosen to be the amplifiers, so thehigh-voltage connectors at the other end of the chamber are at 2700 mm.The centres of the five windows are 283, 816, 1349, 1883 and 2415 mm fromthe amplifiers.78Momentum (MeV/c)140 150 160 170 180 190 200 210Pion Selection Efficiency00. OnlyWith Optimized Cluster CountingWith Suboptimal Cluster CountingFigure 4.24: Variation in PID performance with momentum. Thesethree runs all use the same amplifier with 370 Ω inputimpedance.Most tests were performed at the windows 1349 and 1883 mm from theamplifiers, but a sequence of runs was taken to determine the effect of thesignal propagating along the sense wire. The sense wire voltages were chosenas described in Section 4.2.3 at the middle position, but left unaltered forthe other windows in the sequence. Thus the oscilloscope and amplifiersaturations may change as a function of beam position.The tungsten wire is very thin and has a non-negligible DC resistance(421 Ω for the 20µm diameter wire), so it was expected that the performancewould be better at the windows closer to the amplifiers. Indeed the runstaken at the two windows closest to the amplifiers have slightly higher effi-ciencies (Figure 4.25) than at the two furthest windows, but the differenceis not large. The variation for this small data set is also not monotonic,the second-closest window to the amplifiers shows inexplicably better per-formance than the closest.79Distance from Amplifier2415 mm 1883 mm 1349 mm 816 mmPion Selection Efficiency00. OnlyWith Optimized Cluster CountingWith Suboptimal Cluster CountingFigure 4.25: Variation in PID performance at the different windowsof the prototype. These runs all use the same amplifier with370 Ω input impedance.4.6.7 CablesAs mentioned in Section 4.2.4, we tested two different cable types, and theeffect of adding an additional header connector to simulate needing to feedthrough a bulkhead. Unlike the previous sections, we did not compare theperformance of the cluster-counting algorithms using parameters optimizedon the single run with non-optimal parameters. Thus the individual per-formance numbers may be optimistic, but the comparison between cabletypes can still be done. In Figure 4.26 we show the result from several runsusing an amplifier with 50 Ω input impedance. The low gain columns havethe Chamber A sense wire voltage at 1820 V, while the high gain columnsare at 1835 V. The high gain voltage was chosen according to Section 4.2.3.Since our gain-doubling voltage is approximately 60 V, the low gain columnshave about 84 % the gain of the high gain columns. The voltages are higher801855N 1855Y 179N 179Y 1855N 1855Y 179N 179YPion Selection Efficiency00. Low Gain High GainFigure 4.26: Variation in PID performance using different cable types.The red is the performance using charge integration only, theblue on top is the additional performance gain from combin-ing charge integration and cluster counting. All the runs areat 210 MeV/c and use the same amplifier with 50 Ω inputimpedance. “Y” and “N” designate the presence or absence ofan extra header connector. The first four runs are at low gasgain, and the last four are at higher gas gain.than for the runs described in the earlier sections because the amplifiershave different electronic gain. The cable types 1855 and 179 are describedin Section 4.2.4, while the Y and N designations indicate the presence orabsence of the extra header connector, respectively.A general trend to be noticed is that the high gain columns have no-ticeably better performance than the low gain columns, which is contraryto what was shown in Section 4.6.4. This is likely because these amplifiershave different electronic gains and the selected wire voltages do not lie inthe same performance region as the results shown in Section 4.6.4.The cable type and the inclusion of the header connector only marginally81affect the figure of merit, by an amount less than the typical variation be-tween identical runs and from the track composition process ∼ 5 %. It istempting to see that the 179N columns are the highest between the two sets,but the difference is not nearly as dramatic as the variation due to gas gainor the additional contribution of cluster counting itself.4.6.8 AmplifiersAs described in Section 4.2.2, we tested several types of amplifiers, mostlydistinguished by their input impedance and gain. We remind the readerthat the sense wire voltages used are different for the various amplifiers, andwere chosen to get approximately constant signal amplitude as described inSection 4.6.4.In Figure 4.27, the results from three different amplifiers at two differentpositions along the sense wire are shown. The input impedance of eachamplifier is indicated, and the amplifiers with the same labels are the samefor the two different positions. The 370 Ω “inv” amplifier returns an invertedsignal, while the others do not.There is considerable variation between the amplifiers, but the generalresult is that the 370 Ω amplifiers give the best results. This indicates theimportance of matching the amplifier input impedance with the impedanceand termination of the drift chamber itself. Unfortunately the indicationof the best amplifier is not very strong, as a proper study of the optimalgas gain for each amplifier was not done in this experiment. The variationbetween the amplifiers in Figure 4.27 is of the same order as the variationwith gas gain for a single amplifier shown in Figure 4.23. It is possiblethat the variations seen here are mostly due to gain effects rather than theimpedance and implementation details of the amplifiers.4.6.9 Summary of ResultsThe studies undertaken attempt to explore a multidimensional parameterspace, so the results are difficult to summarize concisely. Here we restatethe lessons learned from each study described above.82Ω50  invΩ370 Ω370 Ω50  invΩ370 Ω370Pion Selection Efficiency00. mm 1349 mmFigure 4.27: Variation in PID performance using different amplifiers.The red is the performance using charge integration only, theblue is the additional performance gain from combining chargeintegration and cluster counting. The upper labels indicatethe beam position along the sense wire, measured from theamplifier. The “inv” label indicates an inverting amplifier.The various cluster counting algorithms all perform roughly equivalently(Section 4.6.2). Their parameters must be optimized for good performance,but the regions of good performance in parameter-space are quite large.Even sub-optimal parameters only give slightly worse performance. Moreadvanced techniques (such as the timeout booster) can compensate for a less-optimized algorithm, but are unnecessary when the algorithm is optimizedproperly.Optimal smoothing for the cluster-counting algorithms is on the orderof a few nanoseconds, indicating that a higher sampling rate is unnecessary.The corresponding Nyquist frequency is on the order of hundreds of MHz.This means that the successful implementation of cluster counting does not83depend on getting overly expensive or customized hardware. Indeed the bestalgorithm studied simply applies a threshold to the second-derivative of thesignal, a process that can be done with analog electronics or in an FPGA.Cluster timing gives results that are slightly poorer than cluster count-ing used alone (Section 4.6.3). When combined with charge integration andcluster counting however, the improvement is minor compared to chargeintegration and cluster counting without the cluster timing. Given the ad-ditional complexity of storing and calculating average cluster timings, thistechnique is unlikely to be worth exploring further.PID performance depends strongly on having the proper wire voltagesand thus gas gains (Section 4.6.4). In some configurations, higher gain is notnecessarily better, but this is dependent on the choice of amplifier. Thus fora given amplifier and equipment configuration, the optimal gas gain mustbe carefully determined.There is not much variation in PID performance as a function of thebeam position along the sense wire length (Section 4.6.6). Since the signalis attenuated while travelling along the sense wire, this effect is coupled withthe gain of the amplifier and the choice of wire voltages.The choice of cable types and additional connectors seems to have a neg-ligible effect on the PID performance (Section 4.6.7). Performance is verysensitive to the choice of amplifier (Section 4.6.8), but this is coupled withthe sense wire voltage. There is a weak indication that matching the ampli-fier input impedance with the impedance and termination of the chamberitself gives better performance.4.7 ConclusionsThe general result is clear: implementing cluster counting increases the par-ticle identification capability of a drift chamber. We make no claim of havingfound the optimal equipment and analysis techniques in the multidimen-sional parameter space that we explored. Thus we can state that clustercounting improves PID performance even in sub-optimal conditions.The absolute improvement in the pion selection efficiency at 90 % muon84rejection is generally around 10 % (e.g., from 50 % to 60 %, and see Fig-ure 4.19). The improvement is greatest when the PID performance fromcharge integration only is poorest, thus making the detector PID responsemore uniform.The optimal smoothing times for cluster-counting algorithms are on theorder of a few nanoseconds, corresponding to a Nyquist frequency of hun-dreds of MHz. Thus successful cluster counting can be accomplished evenwith modest hardware.All future particle physics experiments that use a drift chamber for PIDshould strongly consider a cluster-counting option. This study shows thatperformance gains can be obtained that justify the additional complexityand cost of a cluster-counting drift chamber.4.8 Cluster-Counting AlgorithmsHere are contained precise definitions of the cluster-counting and smoothingalgorithms used in this work. We define a signal or trace as a series ofvoltage samples indexed by a discrete time variable V (t). Though the timevariable has units (in our raw format the units are 50 ps), here we treat itas an integer index. In general, a signal will have N samples indexed withinteger t running from 0 to N − Smoothing ProceduresTwo types of smoothing are used in the algorithms. One involves replacingeach element of the signal by the average of itself and its neighbours, withoutreducing the total number of elements. The other reduces the total numberof elements, and each element’s value is the average of a set of elements inthe original signal.Boxcar SmoothingThe so-called “boxcar smoothing” with n frames substitutes each samplewith the average of itself and the previous n−1 samples. The first n samples85(0 to n− 1) are a boundary case, replaced simply by V˜n(n).V˜n(t) =1nn−1∑i=0V (t− i) t ≥ n,V˜n(n) t < n.(4.3)AveragingThe so-called “true averaging” procedure produces a signal with a reducednumber of samples. For an n-frame averaging, the result is a series of k =N ÷n voltages (floored division), indexed with the integer t¯ running from 0to k.V¯n(t¯) =1nn−1∑i=0V (s+ nt¯+ i) (4.4)Here, n is the number of samples that are averaged, s = N mod n, and Nis the total number of samples in the original trace.This averaging has the potential to “divide” cluster signals if the aver-aging bin edges lie on top of a cluster (Figure 4.15). Thus it is useful to alsoshift the smoothing bins by adding n ÷ 2 to the argument of V inside thesum. If the smoothing is done with and without the shift, it is less likelythat the same cluster will be divided in both cases, compared to doing thesmoothing only one way.4.8.2 Signal above AverageThis algorithm has two parameters: a number of frames for smoothing anda threshold. From the non-smoothed signal at time t is subtracted the n-frame smoothed signal at time t − 1. If the resulting quantity crosses thethreshold ∆ downwards, a cluster is identified at that time.The cluster times found by this algorithm are those t in {max(n, 2)..N}86that satisfy(V (t)− V˜n(t− 1) < ∆) and(V (t− 1)− V˜n(t− 2) ≥ ∆).(4.5)4.8.3 Smooth and DelayThis algorithm has four parameters: two smoothing times, a delay, and athreshold.Two copies of the original signal are smoothed by different amounts (pand q frames) using the “boxcar smoothing”. The q-frame smoothed copyis then delayed by d frames, and the two copies are then subtracted. If theresulting quantity crosses the threshold ∆ downwards, a cluster is countedat that time.The cluster times found by this algorithm are those t in {d..N} thatsatisfyV˜p(t)− V˜q(t− d)d< ∆ andV˜p(t− 1)− V˜q(t− 1− d)d≥ ∆.(4.6)The “Signal above Average” algorithm is a special case with p = 1, q = n,and d = 1. Another special case can be constructed with d = 0 with thedenominator set to 1.It can be shown that if the two smoothing times are equal (p = q),the quantity computed with smoothing q and delay d is identical to thatcomputed with smoothing d and delay q. Thus the parameter range can berestricted to d > q without loss of generality.4.8.4 Second DerivativeThis algorithm has two parameters: a smoothing time and a threshold. Ituses the true averaging procedure rather than the “boxcar smoothing”, sothe time is labelled t¯ as in Section 4.8.1. Simply put, the second derivative87is calculated and compared with a threshold.The second derivative is calculated as follows:V¯ ′′(t¯) =1δ2([V¯ (t¯+ 2)− V¯ (t¯+ 1)]− [V¯ (t¯+ 1)− V¯ (t¯)])(4.7)where δ is the time interval corresponding to the n samples that were aver-aged to do the smoothing.The times of the clusters found with the second-derivative algorithm arethose t¯ in {0..N ÷ n} that satisfyV¯ ′′(t¯) < ∆ and V¯ ′′(t¯− 1) ≥ ∆. (4.8)Because this algorithm uses the true averaging, it suffers from the prob-lem of potentially “dividing” cluster signals between smoothing bins (Fig-ure 4.15). Thus we also implemented a two-pass second-derivative algorithmthat looks for clusters a second time on the averaged signal with a delay ap-plied as described in Section 4.8.1. The numbers of clusters found in eachpass are added together. It is understood that the resulting cluster count isinflated because many clusters will be double-counted, but nevertheless it isan appropriate variable for identifying particles.4.8.5 Timeout BoosterThe so-called “timeout booster” takes as an input the list of clusters foundby one of the above algorithms. It considers these as cluster candidates, andvalidates or rejects each one in turn.For a given cluster candidate, the voltage and time in the original wave-form at which the cluster-finding algorithm was triggered is recorded. Thenfollowing the waveform forward, the voltage is checked to see when it hasrecovered above the recorded value (the pulses are negative). If the voltagerecovered within the timeout window, it is a short-lived pulse and thus re-jected as a fake. If the timeout is reached without the voltage recovering, itis long-lived and kept as a real cluster.88For a list of potential clusters t′i, real clusters satisfyV (t) < V (t′i) for all t in {t′i..(t′i + T )} (4.9)where T is the chosen timeout. The rejection of fake clusters by the timeoutprocedure permits the use of lower thresholds in the original algorithm. Thelower threshold increases the efficiency of finding real clusters (smaller missrate) but increases the rate of detecting fake clusters. The timeout procedurethen eliminates most of the fake clusters, keeping the real ones.89Chapter 5Multi-Cell Prototype5.1 IntroductionIn 2011 the Italian prototype called “proto 2” was constructed at LNF-INFN in Frascati, Italy. Machining and construction of the mechanicalcomponents was done by technical staff at LNF, except for the outer shellwhich was constructed by a commercial firm. The stringing of the 205 wireswas done by hand over the course of several weeks by Giuseppe Finocchiaroand me.All of the assembly was done in a clean room at LNF, and all inner com-ponents were cleaned with acetone. The smaller pieces were also cleanedwith an ultrasonic cleaning tank. The clean room was class 10000-equivalent;the designation refers to the maximum allowed number of dust particlesgreater than 0.5µm diameter per cubic foot. Class 10000 is not particularlyclean as far as clean rooms go, it is only 2 classes cleaner than regular roomair (there are 8 classes cleaner than regular air defined by ISO standards).The cleanliness is mostly important for preventing sparking and ageing be-haviour in drift chambers built to be used for a long time or with very highrates (see Section 2.2 for a discussion of ageing). For prototype work, thiscleanliness is expected to be adequate. Only the wires were omitted fromthe cleaning because of their fragility.The prototype was tested at the M11 beamline at TRIUMF [64]. This is90the same facility that was used in the single-cell prototype study describedin Chapter 4. The beam is composed of positrons, positive muons and pions,and protons. The beam particles have roughly the same momentum for agiven test, and momenta of 140 to 350 MeV were used. In our test we addeda polyethylene absorber to block the protons. The analysis of the data takenduring the beam test is described in Chapter 7.In the following sections we describe the wire materials, layout, andstringing; the outer structure of the prototype; and the electronics used toread the sense wire signals.5.2 WiresThere are 205 wires in total: 28 sense wires, 152 field wires, and 25 guardwires (see Figure 5.1). The guard wires and outer field wires are outside ofthe active cell areas and serve to mimic the influence of an infinite plane ofcells. This makes the fields inside the cells more homogeneous. The guardand field wires are made of bare aluminium, while the sense wires are eithertungsten-rhenium or molybdenum, both gold coated.The wires were inspected with a microscope to determine their surfacequality. The the gold-coated tungsten-rhenium and molybdenum wires werevery smooth, but the bare aluminium wires were observed to have large∼ 50µm protrusions from the surface (Figure 5.2). The protrusions mayhave simply been dust on the wire, but we were unable to identify themwith the microscope. The 80µm diameter aluminium wires had less severedefects than the thicker 120µm wires, so these were mostly used throughoutthe chamber. Some initial outer wires of 120µm diameter were installedbefore the defects were noticed. These were not replaced as they are forguard wires outside the active cells, so their effect should be negligible.As mentioned above, 9 of the field wires used the thicker aluminium,but the rest are all 80µm, and the difference is not expected to change theelectric fields in the cells. The sense wires for cells 0 to 6 used the traditionaltungsten wire, while all others used the molybdenum wire (see Figure 5.1for the cell numbering). The intent was twofold: to evaluate the behaviour91-7-5.6-4.2-2.8-1.401. -4.2 -2.8 -1.4 0 1.4 2.8 4.2 5.6Y (cm)X (cm)FieldGuardSense1900VW-Rh25umMo25um0VAl80um1900VAl80um1490V1680VGas Connectors0 1 2 34 5 67 8 9 1011 12 1314 15 16 1718 19 2021 22 23 2425 26 27Viewed from the high-voltage sideFigure 5.1: Layout of all the wires in proto 2. The type, materials,diameters, and optimal voltages on the wires are indicated inthe legend. The numbers in each cell indicate the numberingsystem used in this work. In the beam tests described in thisthesis, the charged particle tracks come from the top of thefigure and exit through the bottom.92Figure 5.2: Microscope image of the 25µm diameter gold-coatedmolybdenum wire (left) and the 80µm diameter bare aluminiumwire (right). The scales are different.of the molybdenum wire during stringing (e.g., is it easier or harder touse than tungsten), and to compare the performance of the tungsten andmolybdenum cells. The performance analysis was never carried out.To obtain a nominal gravitational sag of 200µm in the middle of thechamber, we calculated the required tension:T =gpir2ρL28S. (5.1)where g is the gravitational acceleration, r is the radius of the wire, ρ is thevolumetric mass density of the wire, L is the length of the wire, and S is thedesired sag [12]. We calculated T/g to find the mass of a weight to be hungfrom one end of the wire to provide the tension. For our prototype, masses of120, 53.0, 39.1, and 21.5 g (grams) were indicated for the thick aluminium,thinner aluminium, tungsten, and molybdenum wires, respectively. Thetotal force on the endplates is thus about 10 kgf (kilogram-force).The wires are all strung parallel to each other, and each is 2.5 m long. Weonly read out the signal on one end of the wire, and the far end is terminatedto prevent reflections, so the parallel wires give no z-coordinate information,i.e., we have no information about the distance of charged particle tracksalong the wire axis. The TRIUMF M11 beam spot size is ∼ 1 cm × 20 cm,93and in all our tests we only expose the chamber to the beam through onewindow at a time, so all our analyses are effectively two-dimensional.5.3 StructureThe aluminium structure and surface defects in the internal aluminiumsurfaces were attached and filled in with a two-part epoxy. This epoxywas the same as used for the LHCb drift tubes (Araldite AY103-1 fromHuntsman[67]). Since the epoxy was black, it was later covered with shinyaluminium tape to maintain a conductive surface and so that the chamberwould not look ugly.Electronic feedthroughs are pin-like devices with an inner hollow metal-lic cylinder and an outer plastic sheath. The inner cylinder can be crimpedto hold the wires, and the plastic sheath’s diameter is such that it fitssnugly into the holes of the endplates. For proto 2, we re-purposed left-over feedthroughs from the KLOE drift chamber [68]. A schematic of afeedthrough with tensioning weight is shown in Figure 5.3.The feedthroughs inserted into the endplate and the wire ends on thefeedthroughs were sealed with acrylic glue. The glue had low viscosity andtended to fill cracks, but may have entered into the drift chamber innersurface before drying. We did not do extensive tests of glues as was donefor BaBar [69]. A photograph of the fully-strung chamber is in Figure 5.4.The outer shell is composed of a 3 mm sheet of aluminium folded intoa rectangular box and welded down a side. Six thin windows are machinedout of the walls to reduce the material exposed to the beam. Photos of theshell can be seen in Figures 5.5 and 5.6. The endplates into which the wirefeedthroughs are inserted are made of a material called permaglass, which isa kind of fibreglass. On top of the permaglass endplates are several layers ofmaterial for supporting the electronics. The design ensures that when theelectronic connectors are connected and disconnected from the wires, theforce is exerted on the feedthroughs and not the wires or crimp pins, whichare fragile.In the lab we tested for gas-tightness using a “sniffer” device, which94Pulley WheelTensioning WeightWireCrimp AreaEndplateT/gFigure 5.3: Schematic of the chamber endplate with a feedthroughinserted, and a tensioning weight applied before crimping.samples the air and beeps when detecting certain gases. We flushed thechamber with pure helium, as this is the smallest gas particle in our mixtureand would most readily flow through leaks. The sniffer was not very reliable(e.g., the readings would fluctuate rapidly, and sometimes would refuse todetect a known gas coming directly from a hose), but we were able to use itto find a few significant leaks and seal them with epoxy.During the gas testing, the helium exiting the chamber was vented witha long thin tube leading to an external window in the lab. Unfortunately itwas overlooked that this long thin tube would offer resistance to the flow of95Figure 5.4: Structural frame and wires of the prototype. Still missingare some endplate components and the outer aluminium shell.helium, much as long thin wire could have significant electrical resistance.At some point the helium gas flow was increased, but rather than flowingout of the tube, it increased the pressure in the drift chamber. The driftchamber is not designed to operate at significant over- or under-pressuresrelative to the atmosphere, and the thin chamber wall at the large centralwindow exploded. A few wires were broken and had to be re-strung, and anew window had to be welded to close the large hole (see Figure 5.6).5.4 ElectronicsConnectors for the high-voltage power supplies are mounted on one end ofthe drift chamber (Figure 5.7). Front-end electronics are mounted on theother end. The front-end electronics are composed of four boards with pre-96Figure 5.5: Photo of the outer shell showing the window positions onproto 2. The window sizes are chosen to admit all angles oftracks that cross the 8 layers of cells, i.e., ±20–30◦.amplifiers, each connected to 7 sense wires in adjacent layers. The amplifierscollect charge (integrated current) and output a voltage proportional to it.Their gain is 8 mV/fC and the rise-time of their pulses is about 2.4 ns [37].The amplifier outputs are connected to digitizers via 10 m long cables (thedesign length of the cabling for SuperB). The digitizer takes the continuousstream of voltage and samples it at 1 ns intervals, producing digital voltagemeasurements that can be easily analyzed using computer programs. Thedigitizer is a commercial CAEN V1742 with a bandwidth of 500 MHz, and12-bit analog-to-digital converters. A photo of the instrumented end of thedrift chamber is shown in Figure 5.8.The completed drift chamber was wrapped in a copper foil that was sol-97Figure 5.6: Close-up photo of the large middle window that exploded,after repair. On the upper left one can also see a repaired cornerin the 3 mm aluminium sheet.dered closed and electrically grounded to the aluminium box. This providesadditional shielding from electromagnetic interference. The whole detectoris mounted on a movable support that can also tilt the chamber along itslong axis. This allows us to take data with tracks at multiple angles in 3dimensions (see Figure 5.9).98SuperB-DCH Servizio Elettronico Laboratori FrascatiLNF SuperB Workshop – December 11Cluster Counting Option: On Detector Electronics – HV distribution boards22G. Felici1MΩ2.2 nFFilter Box [Outside Detector]Distribution Board [number of boards is a function of chamber layer]BOARD #1BOARD #NHV Distribution – dE/dx by means of Cluster Counting  1MΩ500 pF10MΩ Ch 1RT10MΩ Ch 8RT  1MΩ500 pF10MΩ Ch 1RT10MΩ Ch 8RT500 pF500 pF500 pF500 pFAssuming the same general considerations of Charge Measurement Option NB: HV distribution boards should be located on forward end plate and require high frequency ground connection because the termination resistorsMain Power SupplyFigure 5.7: Circuit diagram for the Proto 2 high-voltage connectionson the sense wires. The filtered connection to the high-voltagepower supplies is from the left, and the sense wires are connectedon the right. The termination resistor RT ∼ 300 Ω is chosen tomatch the impedance of the sense wire. There are 8 channels perhigh-voltage connector (only 2 shown here, labelled Ch 1 andCh 8), but only 7 are used in this prototype due to the layoutof the wires. There are 4 connectors for the whole prototype.99Signal cablesAmplifier power cablesBrass shielding Copper foilFigure 5.8: The instrumented end of proto 2, showing the 28 connec-tors from the pre-amplifiers and other electrical connections.The brass box is for shielding.100Figure 5.9: Proto 2 mounted on a movable table and tilting support,for an early beam test at LNF.101Chapter 6Theoretical TrackingImprovementsIn a traditional drift chamber, only the leading edge of the signal from eachcell is used for tracking. The arrival time of the signal relative to a globaltrigger is determined by a threshold algorithm.From calculation, simulations, and calibrations, a time-to-distance re-lation can be obtained, mapping arrival times into distances of the trackfrom a sense wire. Different levels of refinement can be used to improve thetrack distance estimate: information from multiple cells can tell us on whichside of a cell the track passed, corrections can be applied for temperatureand pressure variations in the gas, etc. All such refinements come frominformation outside of the single-cell signals.A tracking refinement exists that uses additional information from thesingle-cell signal itself. If the arrival times of the individual clusters in thesignal are known, a more precise weight can be assigned to the cell whenperforming the global track fit. This section explains how this single-cellimprovement is possible.1026.1 ModelWe use a simple model to illustrate, with the understanding that real driftchambers have many additional complexities that may ruin the effect. Partof this research is to evaluate whether indeed the potential improvements tothe tracking resolution are measurable in a real drift chamber. Our modelconsists of a single infinite cell with a single straight track and a sense wireat the origin. The track is produced instantaneously, as if the particle wasmoving at infinite speed. The model is entirely two-dimensional.We define the impact parameter of the track, b, as the shortest distancebetween the wire and the track (see Figure 6.1). This is also known asthe distance of closest approach. The unique straight line having length bjoining the wire and the track is in general perpendicular to the track itself.The point where this line intersects the track is known at the point of closestapproach. We define Dn to be the distance of the nth ionization event asmeasured along the track from the point of closest approach. The quantityxn is the actual distance of the ionization event from the wire, which is thesum in quadrature of Dn and b: xn =√D2n + b2. For the mathematicalmodels constructed, it is also convenient to define D0, which would be thedistance of a fictitious 0th cluster which always lies at the point of closestapproach and for which x0 = b.Drift chamber electronics do not measure distances, but times of arrivalfor the clusters or signals from the ionization events, however since the time-to-distance relation is monotonic, there is a one-to-one relation betweenarrival times and distances, so the simple model is treated entirely in termsof distances.The final simplification is done without loss of generality. Drift chamberelectronics have no ability to distinguish ionization events produced before orafter of the point of closest approach. In other words, ionization events withDn < 0 look identical to those with Dn > 0. Assuming that the ionizationevents are independent and follow Poisson statistics, we may simply have allionization events occur at Dn > 0 and double the overall ionization density.103D3bx3Figure 6.1: Illustration of the final simplification of the model de-scribed in Section 6.1, and the distances used in the model. b isthe impact parameter of the track, and x3 is the distance of the3rd ionization event from the wire. The figure on the left showsa track with ionization events before and after the point of clos-est approach. The figure on the right is the same track with allionization events “rectified” to occur after the point of closestapproach. The two models are mathematically equivalent, andwe use the simpler right-hand model without loss of general-ity. Another way of stating this is that the model is symmetricunder the operation Dn → −Dn for any n.1046.2 Distances Along the TrackFirst we define the probability density function for the distance of the ficti-tious 0th cluster along the track, which always occurs at D0 = 0:f0(D) = δ(D). (6.1)δ(x) is the Dirac delta function. Since the ionization events follow Poissonstatistics, the probability density function of the separation of two consecu-tive ionizations (∆) follows an exponential distribution.f∆(∆) =ρe−ρ∆ ∆ ≥ 00 ∆ < 0 (6.2)where ρ is double the density of ionization events along the track (explainedat the end of Section 6.1).With Equation 6.1 and Equation 6.2 we can construct the probabilitydensity function for the distance of the first cluster along the track, D1 =D0 + ∆. The probability density function for the sum of two independentvariables is simply the convolution of the two variables’ probability densityfunctions:f1(D) =∫ ∞−∞f0(x)f∆(D − x)dx (6.3)= f∆(D) =ρe−ρD D ≥ 00 D < 0 . (6.4)Similarly we construct the probability density function for the distanceof the second cluster along the track, D2 = D1 + ∆.f2(D) =∫ ∞−∞f1(x)f∆(D − x)dx (6.5)f2(D) =∫ D0 ρ2e−ρxe−ρ(D−x)dx D ≥ 00 D < 0(6.6)105f2(D) =ρ2De−ρD D ≥ 00 D < 0 (6.7)Since ∆ ≥ 0, we can state that Dn ≥ Dn−1 > 0 for all n > 0, andD0 = 0, to avoid overly cluttering page with the piecewise notation.Similarly again we construct D3 = D2 + ∆.f3(D) =∫ ∞−∞f2(x)f∆(D − x)dx (6.8)=∫ D30ρ3xe−ρxe−ρ(D−x)dx (6.9)= ρ3D22e−ρD (6.10)By obvious pattern-matching and familiarity with iterated integrations,we can generalize tofn(D) = ρ(ρD)n−1(n− 1)! e−ρD. (6.11)This turns out to be an Erlang distribution, which is a special case of aGamma distribution with integer shape parameter. These are frequentlyencountered when modelling waiting times and intervals of stochastic pro-cesses.It is important to point out that these distributions for the differentclusters are applicable when entire sorted sets of cluster arrival times areavailable. In other words, if one measures the arrival times of clusters inmany tracks, and for each n makes a histogram of the nth cluster in eachtrack, then the distribution will be described by fn(D) in Equation 6.11 andFigure 6.2.If instead one is searching for clusters in a track and has so far countedn clusters, the procedure to predict the arrival time of the next cluster thecorrect distribution is not fn(D) from Equation 6.11, but instead it wouldbe f1(D − Dn−1), the distribution of the next-to-come cluster given theprevious one:fn(D) = f1(D −Dn−1) (6.12)1060123450 0.5 1 1.5 2 2.5 3ProbabilityDensityDistance from point of closest approach, D (cm)Distances Along Track, ρ=5.0 clusters/cmn = 1n = 2n = 3n = 4n = 5Figure 6.2: Probability distributions of ionization event distancesalong the track.fn(D) =ρe−ρ(D−Dn−1) D ≥ Dn−10 D < Dn−1 . (6.13)This is because the ionization events are Poisson-distributed, and thusthey are uncorrelated. The shape of the probability density function for thenext uncorrelated event clearly cannot depend on the previous events. Itonly depends on Dn−1 because ∆ cannot be negative, so Dn−1 serves as thelower limit and shift factor.6.3 Distances From the WireIn Section 6.2 we found the probability density function for the distance ofthe nth ionization event from the point of closest approach along the track(Dn). The point of closest approach of the track is a distance b away from107the actual wire, a distance also called the impact parameter. We wish toknow the probability density function for the distance of the nth cluster fromthe wire itself.Recalling that we are working in only two dimensions, the distance fromthe wire given a distance along the track isxn =√D2n + b2. (6.14)We exploit the conservation of probability to make the transformation:fn(D)dD = gn(x)dx (6.15)fn(D(x))dD(x) = ρ(ρ√x2 − b2)n−1(n− 1)! e−ρ√x2−b2 x√x2 − b2dx (6.16)thus obtaininggn(x) =ρn(n− 1)!x(x2 − b2)n−22 e−ρ√x2−b2 . (6.17)An interesting feature has emerged in the exponent n−2n , so that thefunctional form drastically changes between n = 1, n = 2 and n ≥ 3. Forexample in the limit of x→ b+ (or D → 0+), we obtainlimx→b+gn(x) =∞ n = 1ρ2b n = 20 n ≥ 3(6.18)It would be interesting to find the critical points and maxima of gn(x),however this is complicated and the precise answers (involving roots of third-order polynomials) are not very enlightening. We can summarize as follows:g1 has a maximum only at x → D+, where it diverges; gn for n ≥ 3 has asingle finite maximum at finite x, the position of which grows slowly with n.g2 has interesting maximal behaviour, strongly dependent on the productρb. Specifically, if ρb ≥ 12 , the only maximum is at the boundary x → b+10802468100 0.5 1 1.5 2 2.5 3ProbabilityDensityDistance from the wire, x (cm)Distances From Wire, ρ = 5.0 clusters/cm, b = 0.5 cmn = 1n = 2n = 3n = 4Figure 6.3: Probability distributions of ionization event distancesfrom the wire.where g2(D) = ρ2b. If ρb < 12 then there are two critical points atx2± =1±√1− (2ρb)22ρ2(6.19)where x+ is generally a local maximum and x− a local minimum. For certainvalues of ρ and b, this local maximum is also the global maximum, while forothers the boundary value at x→ b+ is the global maximum. Unfortunatelyagain the precise expression for these cases is not enlightening.Again it should be noted that Equation 6.17 was calculated assumingthat none of the distances have yet been measured. This is the distributionof distances of clusters one would obtain if one simply made a histogramof the nth measured cluster. In this sense they are “agnostic” probabilitydensity functions.10900.511.522.533.540 0.2 0.4 0.6 0.8 1ProbabilityDensityDistance from the wire, x (cm)Distances from Wire for 2nd Ionization Event, ρ = 5.0 clusters/cmb = 0.0b = 0.025b = 0.05b = 0.075b = 0.1( 12ρ)b = 0.125b = 0.15b = 0.175Figure 6.4: Probability distributions of second ionization event dis-tances from the wire.If the first n ionization events have already had their distances measured,then the probability density function for the distance of the (n+1)th clusteris not gn+1(x) given by Equation 6.17 but rather a form of g1(x) shifted bythe position of the last measured cluster:hn(x) =xnρe−ρ(√x2n−b2−√x2n−1−b2)√x2n − b2. (6.20)This can be obtained by performing the conservation-of-probability calcula-tion to convert Equation 6.13 to refer to xn rather than Dn.1106.4 Bayesian AnalysisIn Section 6.3 we found the probability distribution functions for the distanceof the nth ionization event from the wire, given a known impact parameterb. In a drift chamber experiment, the situation is reversed. There the arrivaltime of the electron cluster from the nth ionization event is measured andconverted into a distance using the time-to-distance relation for that driftchamber cell. From this distance we wish to know the most likely value forthe unknown impact parameter. With Bayes’ theorem, we can obtain thefull probability density function for the impact parameter, given measureddistances {xn}.Bayes’ theorem statesP (α|β;σ) = P (α;σ)P (β|α;σ)P (β;σ)(6.21)where the left hand side is the posterior probability distribution: the prob-ability of an event α given the observed state β and external assumptionsσ. The first term in the numerator is the probability of event α given ex-ternal assumptions σ irrespective of the observation β; this is also calledthe “prior probability” or just the “prior”, because it refers to the state ofthe experiment before a measurement is done. The second term in the nu-merator is the probability of observing β given the state α and assumptionsσ; this term is called the likelihood. The denominator is the probability ofobserving β under assumptions σ irrespective of the state α; the denomi-nator is essentially a normalization constant, and is just the integral of thenumerator over all possible values of α.In our case, the left hand side is the probability distribution function forthe impact parameter b given a set of observed ionization distances from thewire {xn}. The first term in the numerator is the prior probability distri-bution for the impact parameter, while the second is the previously foundprobability distribution function for the distances of the ionization eventsfrom the wire, given in Equation 6.17. The denominator is the probabilityof getting a set of measured distances xn irrespective of the true impact111parameter; as mentioned this normalization term is just the integral of thewhole numerator over all possible values of the impact parameter.Bayes’ theorem is very general and in this case we apply it iteratively tobuild up the probability density function considering one ionization eventat a time.6.4.1 The First ClusterWe calculate the probability density function of the impact parameter bgiven the measured distance from the sense wire of the first ionization eventx1. Without any additional information, the prior probability density func-tion for the impact parameter is uniform over all positive values. In princi-ple this should be restricted to the actual dimensions of the drift chambercell volume, though here we maintain the infinite-cell approximation for thecalculation. The approximation should have little impact, since we only con-sider the first few clusters, which necessarily originate closest to the wire.This renders our prior probability distribution function unnormalizable byitself (since its integral diverges), but the denominator in Bayes’ theoremfixes this problem automatically.We getP (b|x1; ρ) = Cg1(x1)P (x1; ρ)(6.22)where C is the previously-mentioned unnormalizable term and g1 is takenfrom Equation 6.17. Next we calculate the denominator, which isP (x1; ρ) =∫ ∞0Cg1(x1)db (6.23)=∫ x10Cρx1(x21 − b2)−12 e−ρ√x21−b2db. (6.24)We make the substitution z =√x21 − b2 to simplify the expression and use112the popular mathematics program Wolfram Alpha [70] to obtainP (x1; ρ) = Cρx1∫ x10e−ρzx21 − z2dz= Cρx12pi(I0(ρx1)− L0(ρx1)).(6.25)where I0 is the modified Bessel function of the first kind at 0th order, andL0 is the modified Struve function at 0th order. The difference of the twospecial functions does not reduce to any other special function, but theirTaylor series can be combined in a simple way (Appendix A.5).Thus the final expression for the probability density function of the im-pact parameter b given a measured distance of the first ionization event fromthe wire x1 isP (b|x1; ρ) = Cρx1(x21 − b2)−12 e−ρ√x21−b2Cρx1pi2 (I0(ρx1)− L0(ρx1))(6.26)=2e−ρ√x21−b2pi√x21 − b2(I0(ρx1)− L0(ρx1)). (6.27)As stated, the unnormalizable term C cancels out, which is a generic featureof Bayesian analysis. Note that the function is only defined for b < x1,beyond this the probability density is zero.A plot of Equation 6.27 is shown in Figure 6.5 with three different val-ues of x1. Unfortunately the numerical calculation becomes unstable withrealistic values of ρ in the usual units (cm). Thus this and later plots use“dimensionless” units with ρ = 1. The reader may wish to interpret theunits of ρ in clusters/millimetre and b in millimetres. In each case, themost likely value for the impact parameter is exactly the distance of thefirst cluster, and the shape of the function does not change. Indeed the onlyparameters in Equation 6.27 are the cluster density and the first clusterarrival time. The cluster density is considered fixed, but does vary slightlywith the particle species, though that information is not available at thetime of measurement.1130.5 0.6 0.7 0.8 0.9 1 1.1 1.2110Impact parameter bProbability density = 0.81x = 11x = 1.21xFigure 6.5: Plot of the probability density function of the impact pa-rameter b when considering only a single cluster. The plot showsthree different distances x1 from the sense wire. The mean clus-ter density of ρ = 1.6.5 The Second ClusterTo consider the information in the second cluster, we simply use Bayes’ the-orem again, but now the prior probability is the one shown in Equation 6.27and the likelihood term is Equation 6.20 with n = 2. In equations:P2(b|x2;x1, ρ) = P1(b|x1, ρ)P (x2|b, ρ)P (x2|x1, ρ) (6.28)where P1(b|x1, ρ) is exactly Equation 6.27 andP (x2|b, ρ) = ρx2 e−ρ(√x22−b2−√x21−b2)√x22 − b2. (6.29)The denominator is again calculated by taking the integral of the whole114numerator. As with the unnormalizable term C in Section 6.4.1, the con-stant parts of the numerator cancel out with the denominator, since theyfactor out of the integral. We are left withP2(b|x2;x1, ρ) = I2(b, ρ, x1, x2)∫ x10 I2(b, ρ, x1, x2)db(6.30)whereI2(b, ρ, x1, x2, ) =e−ρ√x22−b2√x21 − b2√x22 − b2. (6.31)Unfortunately no closed form expression is available for the integral.Fortunately numerical methods are readily available. We use the defaultGSLIntegrator method through the ROOT wrapper functions, as they arerecommended for general use and this function is not particularly nasty [2, 3].The resulting function has three parameters: ρ which we consider fixed,x1, and x2. The plot in Figure 6.6 shows Equation 6.30 computed numer-ically with different values of x2, alongside Equation 6.27 computed withthe same x1 value. The main feature is that the most likely value of b isnever affected by the position of the second cluster, but that the shape ofthe distribution is affected. Depending on the position of the second cluster,the probability density for b is shifted either away from or towards the mostlikely value. If the second cluster is in an unlikely place (e.g., very closeto x1 or very far away from the wire) then the width of the distribution isenhanced. If the second cluster is in a more usual place (e.g., within ∼ 1/ρof x1) then the peak at the most likely value is sharper. This translatesdirectly into increased or decreased confidence in the measured value of theimpact parameter.6.6 More ClustersThe process to include even more clusters is the same as in Section 6.5: theprior is the result of the previous calculation, the likelihood is Equation 6.20with the appropriate n, and the denominator is the integral of the numeratorover b from 0 to x1.1150.7 0.75 0.8 0.85 0.9 0.95 1110Impact parameter bProbability density = 11First Cluster Only x = 1.122nd Cluster x = 222nd Cluster xFigure 6.6: Plot of the probability density function of the impact pa-rameter b when considering the first two clusters. The blackcurve uses the result from Equation 6.27 which only considersthe first cluster time. The other two curves use the result fromEquation 6.30 considering also the second cluster, at two differ-ent 2nd cluster times. The mean cluster density is ρ = 1.The calculation is done numerically again, and the function to be inte-grated is only slightly more complex:P3(b|x3; ρ, x1, x2) = J3(b, ρ, x1, x2, x3)∫ x10 J3(b, ρ, x1, x2, x3)db(6.32)whereJ3(b, ρ, x1, x2, x3) =e−ρ√x23−b2√x23 − b2√x22 − b2√x21 − b2. (6.33)116One can see a pattern emerging, whereJN (b, ρ, x1, ..., xN ) =e−ρ√x2N−b2∏Nk=1√x2k − b2. (6.34)The result is shown in Figure 6.7 for fixed values of ρ, x1, and x2 with twodifferent values of x3. The corresponding P1 and P2 curves are again shownfor comparison. It is unfortunately difficult to see the differences between thecurves since they are all somewhat similar. The general trend continues fromthe consideration of the second cluster: the extra cluster does not change themost likely value, but can affect the width of the probability distribution.If the third cluster is in an unlikely place, the width is increased, but if itis consistent with the average cluster density, the width is reduced. Themagnitude of the effect from considering the third cluster is on the sameorder as the change from considering the second cluster.6.7 SummaryThe model presented in this chapter is much too simplified and abstract tomake quantitative predictions that are useful for a real drift chamber pro-totype. The simplicity however strengthens the general qualitative resultsthat directly motivate the study of cluster counting for tracking purposes.The main result is that indeed there is something to be gained in con-sidering clusters beyond just the first one. While the most likely value ofthe impact parameter given a set of cluster distances is only dependent onthe first cluster’s position, the shape of the posterior distribution is affectedby the distances of the later clusters. The generic result is that the width ofthe posterior distribution for the impact parameter b is enhanced when thelater clusters are in extremely unlikely places given the average cluster den-sity. If the later clusters are in likely places, the width of the distribution isreduced. The width of the distribution is directly related to our confidencein the measurement of b.1170.7 0.75 0.8 0.85 0.9 0.95 1110Impact parameter bProbability density = 11First Cluster Only x = 1.521st & 2nd Clusters only x = 1.633rd Cluster x = 2.533rd Cluster xFigure 6.7: Plot of the probability density function of the impact pa-rameter b with a mean cluster density when considering thefirst three clusters. The black curve uses the result from Equa-tion 6.27 which only considers the first cluster time, the bluecurve uses the result from the first two clusters. The red andmagenta curves use the information from the first three clustersat two different 3rd cluster times. The average cluster densityis ρ = 1.118Chapter 7Tracking7.1 OverviewThis chapter deals with the analysis of data taken at TRIUMF in 2012 usingthe Italian prototype proto 2. All the coding and analysis presented here wasdone by me, including the implementation of traditional and cluster-basedtracking algorithms. As with the particle identification study presentedin Chapter 4, the cluster-based technique is used in combination with thetraditional method to try to get better performance.The traditional tracking procedure is as follows. First, the arrival timesof the various signals on the sense wires are determined (Section 7.2). Then,time-to-distance relations are produced using simulations (Section 7.3). Theseare used with the arrival times to determine how far the track passed fromthe various sense wires, and subsequently the track parameters are deter-mined (Section 7.4). Using the self-consistency of the tracks, the time-to-distance relations are improved (Section 7.5) and the tracks parameters arere-evaluated. This refinement process iterates two times, after which the fi-nal resolution of the prototype drift chamber can be measured (Section 7.8).The track parameters are determined using the information from all thecells that have signals except one. A special cell (number 12 in Figure 5.1)is excluded from the computation. This cell is chosen because it is centralin the detector. A statistical analysis is performed of the difference between119the track distance from cell 12’s sense wire according to the fit using theother cells and from the information from cell 12 alone (Section 7.5). Thisis used to generate empirical corrections to the original time-to-distancerelations that were computed theoretically from simulations. With thesecorrections in hand, we re-interpret the arrival times using the new time-to-distance relations and re-do the track fit procedure. This is iterated onemore time to obtain 2nd-order corrected tracks. In the statistical analysis ofthe difference between the information from cell 12 and the information fromthe other cells, the standard deviation gives us a measure of the chamber’sresolution. This is the final result of the traditional tracking: the resolutionof the drift chamber.Next we implement a cluster-counting algorithm (Section 7.6) and try touse the additional information to improve tracking. Here we don’t use justthe number of clusters, as in particle identification, but the individual arrivaltimes of each cluster. Similar to the traditional time-to-distance relations,we build up histograms that characterize the distributions of cluster timesat different track distances. Then we re-interpret the cluster times by asking“for which track distance is this set of cluster times most likely?” Similarto the particle identification study in Chapter 4 (Section 4.5.3), we form acombined likelihood using the traditional information and the cluster times(Section 7.7). The final measured scatter between the track distance and thedistance inferred from cell 12’s signals (traditional and cluster information)gives us the new resolution.What we found is that the resolutions of the drift chamber using tradi-tional tracking and the combined traditional and cluster-counting techniqueare equivalent. If there is any difference, it is not measurable given theuncertainties in our results (Section 7.8).7.2 Measuring the Arrival TimesMeasuring the arrival time of a signal is non-trivial, because there are manyfluctuating factors to account for. The amplitude of the initial clustercan very tremendously, because of the statistical nature of the ionization120avalanche near the wire. Similarly, the baseline voltage (the relative 0 Vpoint) can drift slowly over time, and the signal itself has noise.To deal with the drifting baseline voltage and the regular signal noise,we first note that our trigger system is set up so that no real pulses are everrecorded in the first ∼ 200 ns of each signal (see Figure 7.1). The baselinevoltage drift is slow, so we treat it as constant for each event, but it maydrift between events. Large changes are actually only observed betweenentire datasets that were taken after changing voltages or other settings.Thus we take the average voltage over the first 100 ns of the signal as thebaseline. After this, all voltages are referred to relative to this baseline, notrelative to 0 V. In the same 100 ns region, we calculate the root-mean-square(RMS) deviation from the mean (i.e., the standard deviation). We use thisRMS voltage as a measure of the regular noise on the signal.Since the signal pulses from charge clusters have widely varying am-plitudes, we must carefully select a threshold above which we recognize asignal. If the threshold is too high, we will miss pulses that have smallamplitudes and ruin the time measurement. If the threshold is too low, wemight accidentally identify a random noise spike as the first cluster, againruining the measurement.To resolve this, we use thresholds that are proportional to the RMS noisemeasured in the initial parts of the signal. It was found that thresholds of 4and 10σ were low enough to catch nearly all signals, and 10σ is clearly highenough to almost never trigger on a noise spike. With this threshold, onlyone out of every 6.6×1022 voltage samples should ever exceed the thresholddue to noise, assuming a Gaussian model.We use two thresholds because a single threshold gives a biased measure-ment dependent on the amplitude of the signal, since the threshold crossinggenerally occurs somewhere on the leading edge of the signal. The twothreshold crossings are used as points to do a straight-line extrapolationback to the baseline voltage. The point where the extrapolated line crossesthe baseline is taken to be the arrival time (see Figure 7.1).Recall that no real signal pulses arrive for the first∼ 200 ns of each signal.We wish to identify precisely the earliest possible time that signal pulses can121Time (ns)0 200 400 600 800 1000Voltage (mV)20040060080010001200Figure 7.1: Example signal from a cell in proto 2. The small boxover the first 100 ns shows the baselining and noise measure-ment region. The height of the box is 1σ of noise. The threearrows show the upper and lower threshold crossings, and theextrapolated arrival time at the baseline.arrive. This time would correspond to clusters ionization events immediatelyadjacent to the sense wire. To do this, we build up a histogram of all thearrival times in a data set. At first, individual histograms were collected foreach wire and for different detector configurations, but it was realized thatthey were all identical. Figure 7.2 shows the distribution of arrival times forall wires in a given data set. The sharp leading edge corresponds to thoseionization events that occurred near the sense wire. The other structurerelates to the cell geometry. The population above the “knee” at ∼ 450 nscorresponds to tracks that do not cross the full width of the cell.To obtain a precise measurement of the leading edge of the arrival timedistribution, we take the bin-by-bin derivative and fit a Gaussian function122t0 (ns)0 200 400 600 800 100002000400060008000100001200014000160001800020000Global t0Figure 7.2: Raw arrival time distribution for all signals in all wires.(see Figure 7.3). The central value of this Gaussian distribution correspondsto the point on the leading edge with the greatest slope, and we take this asthe global 0 ns time reference. This is a standard procedure when calibratingdrift chamber signal arrival times [71].In a later study we tried deviating from this time reference by a fewnanoseconds in each direction, because it was realized that possibly the real0 ns time might correspond to some other point on the leading edge, notjust the point with the highest slope. Eventually a slightly different value(164.229 ns) was chosen as this was found to slightly improve the strangedistribution of track distances observed in the data (see Section 7.4).With a global time reference, we can now shift all the arrival time mea-surements so that they are relative to this value. This way signals corre-sponding to tracks essentially hitting the sense wire will have arrival times of∼ 0 ns, and signals from tracks further away from the wire will have arrival123t0 (ns)120 140 160 180 200-50005001000150020002500Calculated Offset: 159.778Sigma: 2.92498Hardcoded Offset:  164.229Derivative dt0Figure 7.3: Derivative of arrival time distribution for all signals inall wires. This shows only the part on the leading edge, anda Gaussian fit. The mean and standard deviations from theGaussian fit are labelled “Calculated Offset” and “Sigma”. The“Hardcoded Offset” is the actual time offset used in the calcu-lations.times up to ∼ 500 ns. The next step is to convert these shifted arrival timesinto distances using the time-to-distance relations.7.3 Garfield Time-to-Distance RelationsTime-to-distance relations are basically mathematical functions that con-vert the arrival time of a signal pulse into the distance of closest approach.That distance is measured between the point of closest approach of the high-energy charged particle crossing the drift chamber and the sense wire (seeFigure 7.4). Because of the statistical nature of the ionizations along thetrack, the actual point at which the first recorded ionization event was pro-124Figure 7.4: Illustration of the terms point and distance of closest ap-proach. The distance of closest approach is also called the im-pact parameter.duced may not be the point of closest approach. Thus the time-to-distancerelation converts an arrival time into the most likely distance for the track.The uncertainty in the measurement is considered when making further cal-culations.We use the computer program Garfield [4] to simulate our prototype andproduce theoretical time-to-distance relations. Garfield is a commonly usedtool for simulating gaseous ionization detectors, including drift chambers.It was used in the design of the prototypes described in this thesis by cal-culating required wire voltages under various conditions (e.g., with different125gas mixtures).Garfield simulates individual track events in the chamber. The tracks allhave a chosen angle of incidence, and a chosen progression of distances fromthe wire. For each sense wire, a histogram is built up of the arrival time dis-tribution for small intervals of distances. Garfield prints the mean and RMSof the histogram, along with tables of bin centres and contents. The printedGarfield log file is used to reconstruct the histograms in ROOT [3]. If thehistograms were reasonably Gaussian, we could just use the printed meanand RMS values. For tracks near the sense wire the distribution is notice-ably non-Gaussian, so the mean and RMS values do not properly describethe distribution. Thus we use the full histograms and fit the arrival timedistributions with Novosibirsk functions (Figure 7.5). The peak location isused instead of the histogram mean, and the full-width at half-maximum isused to obtain the resolution instead of the RMS. The Novosibirsk functionand the choice of the width parameter is described in detail in Appendix A.1.The process of using simulated tracks at known distances to determinethe distribution of arrival times is very similar to what would be done withan external tracker [72, 73]. If we had an external tracking device (e.g.,coincidence counters with narrow windows, or another gaseous detector),we could generate these distributions empirically with real particles from atest beam or from cosmic rays.The reader may have noticed that although we require a function thatconverts an arrival time into a track distance, Garfield has provided ar-rival time distributions for given track distances. The same problem wouldbe encountered if we used empirical distributions from an external tracker.In short, Garfield provides distance-to-time relations, but we require the in-verse. Fortunately the relations are monotonic (i.e., the electrons never driftaway from the sense wires), so the inversion is mostly a trivial flipping ofthe x and y axes. An example of a distance-to-time relation and resolutionplot are shown in Figure 7.6.126s)µArrival times of tracks (0 0.005 0.01 0.015 0.020102030405060708090100x_0 = 0.0 cm Mean   0.003533RMS    0.004479Skewness   1.645s)µArrival times of tracks (0.18 0.19 0.2 0.21 0.220246810121416182022x_0 = 0.5 cm Mean   0.1995RMS    0.005616Skewness  0.6815Figure 7.5: These two plots show the Novosibirsk fits to the arrivaltime distributions for 0◦ tracks at two different distances froma sense wire.7.3.1 InterpolationGarfield only produces histograms of the arrival times for specific requestedtrack positions. We use an interpolation technique to evaluate the time-distance relation and resolution functions in between the track positionsconsidered by Garfield.It is crucial for the interpolation technique to guarantee monotonicitybetween the points, because the original data are the expected signal arrivaltimes and uncertainty as a function of track distance. In the analysis we willneed the inverse: the track distance and its resolution as a function of signalarrival time. Thus the initial interpolated functions and their derivativeswill be inverted and manipulated. If our interpolation functions are non-127DOCA (cm)-0.6 -0.4 -0.2 0 0.2 0.4 0.6Resolution (um)100150200250300350400ResolutionDOCA (cm)-0.6 -0.4 -0.2 0 0.2 0.4 0.6Arrival time (us) to Time RelationFigure 7.6: Resolution and distance-to-time relation calculated byGarfield. This is for the intended SuperB gas of 90 : 10 helium-isobutane mixture. The cell boundaries are at ±0.7 cm. Eachpoint corresponds to a set of Garfield-simulated tracks at a giventrack distance. The most likely arrival time of signal pulses andthe widths of the distributions are the y-values of the lower andupper plots, respectively.128monotonic between the data points, the derivatives will go to zero and thiswill cause nonphysical spikes to plus or minus infinity in the final function.Unfortunately the ROOT software only comes with a one interpolationtype that guarantees monotonicity between the points: a linear interpo-lation. We wish to use a more advanced technique, where monotonicitybetween the points is guaranteed, but which uses curves instead of straightline segments. This is provided by using the so-called Steffen interpolationtechnique [74]. Monotonicity is guaranteed by sacrificing the smoothness ofhigher-order derivatives, but Steffen’s method maintains continuity of thefunction itself and its first derivative. The technique also avoids problemspresent in other interpolation methods such as instability, where a smallchange in a single point can produce large changes in the interpolation func-tion. A plot showing the interpolations using several techniques is shown inFigure 7.7.I implemented Steffen’s interpolation method using the C programminglanguage as a contribution the GNU Scientific Library (GSL) [2]. It willbe available to the public sometime in 2015. Minor modifications had tobe made to the ROOT source code to use the new method, which will becontributed to the ROOT project once the new GSL version is released.7.4 Track FittingWith the time-to-distance relations in hand, we can convert the signal arrivaltimes into distances of closest approach. Although we know the most likelydistance of closest approach (and the uncertainty), we do not yet know theactual angle of the track. Thus we effectively have around each sense wirea circular locus of points to which the track should be tangent.With the signals from multiple cells, the track should be tangent to all thecircles at once, and this is how the ambiguity is resolved (see Figure 7.8). Inreality, a track tangent to all the defined circles will be impossible to obtain,because the circles are at the most likely distance of closest approach, butthe actual track distance can fluctuate.Given the most likely distances xi and their uncertainties ∆xi, we use129Figure 7.7: A comparison of a few interpolation methods using ran-domly generated data points. The data points are the redsquares. Large oscillations are apparent in the cubic spline, andless severe ones are also visible in the Akima technique, whichis already available in GSL and ROOT. The Steffen methodpreserves monotonicity.a computer program to minimize the well-known χ2 function to find thebest-fitting track:χ2 =∑i1N − 2(Di − xi∆xi)2. (7.1)Here the sum over i is over the N active cells from which we extracted arrivaltimes and determined distances of closest approach. Di is the distance ofclosest approach for the proposed track from the wire in cell i. In our teststhe tracks are straight lines in two dimensions, since there is no magneticfield to curve the tracks and we have no information about the z-coordinate,so xt depends on two track parameters: θ, the angle of the track relative1300205091216192326Figure 7.8: Circles to which the track should be tangent, determinedfrom the signal arrival times and the time-to-distance relations.Each cell actually has three concentric circles: the middle cor-responds to the most likely distance, while the inner and outercorrespond to that distance plus and minus one standard devi-ation, respectively.131Figure 7.9: Diagram showing track parameters. See text for mathe-matical the horizontal, and x0, the x-coordinate of the track at y = 0. Thedependence isDi(x0, θ) = Yi cos θ + (x0 −Xi) sin θ, (7.2)where Xi and Yi are the coordinates of the sense wire in cell i. The derivationcan be found in Appendix A.2, and an illustration in Figure 7.9.The best-fitting track corresponds to that choice of x0 and θ which min-imize χ2 as defined in Equation 7.1. The uncertainties in these parametersare found from the derivative of the χ2 function at the minimum. The min-imization and returning of the uncertainties is done by the Minuit2 routinein ROOT [3].7.4.1 Track Initial ParametersReasonable initial track parameters must be chosen in order for the fittingprogram to work properly. For the track angle θ, we note that all of ourdata runs were taken with the beam at a specific angle to the chamber: 0,13222, or −22 degrees. Since we only analyze data sets with a single alignmentangle at a time, we simply use the angle appropriate for the selected dataset. In an experiment with tracks at all possible angles, a simple heuristicalgorithm would be sufficient to provide an initial guess.The initial estimate of the parameter x0 is a function of the sense wirecoordinates of each active cell, and of the initial track angle estimate. If thesense wire coordinates are (Xi, Yi) for cell i, the initial x0 value isx0 =1W∑active1σi(Xi − Yitan θ)(7.3)where σi is the resolution at the location of the track in each cell, used asa weight, and W is sum of these weights. The sum is only done over activecells.In the case of vertical tracks, the denominator tan θ is infinity, so theexpression is just the weighted average of the Xi values. For non-verticaltracks, this is the weighted average of the x-coordinates of the sense wirestranslated down to y = 0 along a line parallel to the track. This is illustratedin Figures 7.10 and 7.11 below.7.4.2 Minimization TroublesAlthough a robust algorithm was used for track minimization, the 2-dimensionalparameter space that must be searched for the best track has multiple lo-cal minima. These are parameter choices that appear to be well-fittingtracks, but that are not the best available. The standard algorithm is notvery good at choosing between minima, and sometimes returns less-than-optimal tracks. To try to alleviate this, I produced “heat” maps like the oneshown in Figure 7.12. Unfortunately I originally used the default ROOTcolour scheme which uses a rainbow spectrum. The rainbow spectrum iswell-known to be terrible for human recognition of features [75]. With therainbow map, the local minima were invisible, and the minimization pro-gram gave terrible results. A comparison of the two colour schemes can beseen in Figures 7.12 and 7.13.133-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1-0.8-0.6-0.4-, Y1)(X2, Y2)(X3, Y3)XYFigure 7.10: Schematic of x0 calculation for vertical tracks. x0 is theaverage of the X coordinates of the active sense wires.An example of two tracks, one of which is a local minimum in the track-parameter space can be seen in Figure 7.14. The local minima arise becauseof the geometry of the cells and the ambiguity about which side of the cellsthe track lies. This results in local minima that tend to be spaced somewhatpredictably on the x0-θ plane. Thus once the regular algorithm has found aminimum, additional minimizations are initiated ±0.7 cm and ±0.15 radiansaway. In cases where these new minimizations find new minima, their χ2values are compared and the best one is taken. This generally finds theglobal minimum, and is a simple way of finding the global minimum in acomplicated function.134-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1-0.8-0.6-0.4-, Y1)(X2, Y2)(X3, Y3)XYFigure 7.11: Schematic of x0 calculation for non-vertical tracks. x0 isfound by translating the coordinates of the active sense wiresparallel to the track until they reach Y = 0, then taking theaverage of the resulting X coordinates.7.4.3 Track Parameter UncertaintiesWe would like the track fitting to have a negligible contribution to the overallresolution of the drift chamber. D is the distance of closest approach of thebest-fit track to a reference cell’s sense wire, and ∆D is the uncertainty inthat value. Both are functions of the track parameters x0 and θ and theirrespective uncertainties. We use cell 12 as the reference cell, because it is inthe centre of the prototype and is also used in the next section to improvethe time-to-distance relations (Section 7.5).If ∆D is large compared to the overall tracking resolution, then thetrack fitting algorithm itself or the geometry of the chamber needs to bemodified to improve the resolution. If ∆D is small compared to the overall135Track x0 (cm)-1.5 -1 -0.5 0 0.5Track Theta1. Mean x  -0.5188Mean y   1.609RMS x   1.003RMS y  0.3085210310410Init fit: 72.4442From fit: 18.5356From grid: 25.213Figure 7.12: Heat-map of the function to be minimized to find thebest track. The darker the colour, the better the track. Thecolour scale is logarithmic. The upwards- and downwards-pointing green triangles are the initial fit parameters and min-imum found by the algorithm, respectively. The asterisk sym-bol is a crude minimum found by a regular grid-search algo-rithm. The function values at those three points are printedabove the plot. A local minimum that is not the global min-imum is indicated by a small blue square in a cloud of darkthat is slightly separated from the true minimum.136Track x0 (cm)-1.5 -1 -0.5 0 0.5Track Theta1. Mean x  -0.5188Mean y   1.609RMS x   1.003RMS y  0.3085210310410Init fit: 72.4442From fit: 18.5356From grid: 25.213Figure 7.13: The exact same function as plotted in Figure 7.12 butusing the default ROOT rainbow colour scheme. The slight“clouds” visible in that figure (local minima) are completelyobscured here.1370004081215 16192327Figure 7.14: Illustration of two potential track candidates. The thintrack in black is the local minimum found by the algorithm,while the thicker line in purple is a better minimum found bya simple grid-search.138resolution, then we can conclude that most of the uncertainty comes fromthe single-cell resolution. In this case, we can attempt to improve the single-cell resolution through more accurate time-to-distance relations and throughcluster counting. We expect ∆D to be small from geometric arguments:the track parameters are derived from N measurements, while the single-cell resolution clearly comes from only one measurement. While the Nmeasurements are not all independent, we can roughly expect a ratio of∼ 1 : √N between ∆D and the single-cell resolution. N is the number ofcells participating in the track fitting, which in our prototype is ∼ 8 fortracks crossing the whole detector.Strictly speaking, the parameter uncertainties extracted from the χ2minimization procedure are only a good choice if the xi values and theiruncertainties follow Gaussian distributions, which they do not when thetrack is very close to the sense wire. Nevertheless they are used in order toavoid further complicating the process, and since the final resolution mea-surement that we wish to obtain is not greatly influenced by the individualtrack parameter uncertainties. The proper method would be to replace theχ2 minimization with a maximum-likelihood method that uses the Novosi-birsk function, then see what variation of parameters would yield a changeof +1/2 in the likelihood to find the 1σ uncertainty.From the slightly-improperly calculated uncertainties in x0 and θ, wecan calculate the uncertainty in ∆D. The equation for it can be found inAppendix A.2. ∆D is the uncertainty in D from the track fitting procedureitself, i.e., it is the shallowness of the “bowl” in the 2D χ2 function that isminimized to find the track. Typical values for ∆D are ∼ 40µm, while theoverall resolution of the drift chamber is ∼ 200µm (shown in Figure 7.16).While this means that ∆D is not negligible, the uncertainty is certainlydominated by the single-cell resolution.1397.5 Iterative Refinement and ResolutionMeasurementOnce the track parameters and uncertainties have been determined, we canquantify the performance of the detector. Normally this would be doneusing some kind of external tracking system, to compare the drift chamber’smeasurement with a known-good measurement. This is similar to whatwas done in Section 4.5 by comparing the drift chamber’s measurementof the energy loss and cluster count to an external time-of-flight system’sidentification of the particles. In the case of proto 2, no external trackerwas available. There was an external tracker built, but it stopped workingshortly before proto 2 was shipped to TRIUMF for the beam test.Fortunately we have another tool at our disposal: self-consistency of thetracks. The measurement of the track parameters using N single-cell signalsshould be about 1/√N better than the single-cell resolution itself. The trickis to perform the track fit using only 7 layers of cells. This provides a “knowngood” measurement of the track parameters against which we can comparethe measurement from the single excluded cell. Though the uncertainty inthe track fit using the 7 layers is non-negligible, the dominant uncertaintywill still be the single-cell resolution. This is very similar to the processused to calibrate the BaBar drift chamber [38]. The cell in proto 2 chosenfor this process is number 12, which is the most-central cell in the chamber.See Figure 5.1 for the wire layout.To measure the resolution using this method, we make histograms of thedifference between the most-likely track distance according to cell 12 andthe distance of the track from cell 12 according to the fit using the other7 layers (Figure 7.15). We exclude tracks that did not cross cell 12. Thesehistograms are made for small intervals of track distances (i.e., distancesaccording to the 7-layer fit). These histograms generally have a Gaussianshape, so we take the mean and standard deviations of Gaussian fits. Thestandard deviation is our measurement of the resolution of the chamber atthat distance from the cell. The mean is a measure of the bias of our time-to-distance relation compared to the “known good” measurements from the140Cell 12 distance - Track Distance (cm)-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5020406080100120140160180200220Track Fitting ResidualsFigure 7.15: Two tracking residual distributions superimposed. Thepeak on the left is for tracks within 0.003 cm of the wire,while the peak on the left is for tracks between 0.259777 and0.26777 cm of the wire. The Gaussian fit functions are shownon top.other cells.Having measured the bias of the time-to-distance relation, we can sub-tract the bias from the original time-to-distance relation (from simulationonly) as a correction. We can then re-process the data and re-do the trackfits, which should improve the tracks. The procedure can be iterated tofurther improve the tracks. We do two iterations of these improvements, asthe average correction is already zero at the second iteration. Figure 7.16shows the resolution and the corrections for the 3 iterations. 0th order iswhat we call the process before any improvements are applied, i.e., usingjust the simulation-produced time-to-distance relation. The sharp cornersin the correction functions near the sense wire are to maintain the constraint141that signals that arrive at 0 ns are identified with 0 mm distance from thewire.Like the Garfield program, our corrections and resolutions are done forsmall intervals of track distance from the wire. For use in the actual trackfitting process, we need a continuous function. For the original Garfieldtime-to-distance relation we used the monotonic Steffen interpolant. In thiscase it was desirable to use relatively low-order piecewise polynomials. Nolibrary could be found that provided piecewise-continuous polynomials withcontinuous derivatives, so I coded one myself.During the iterative improvement process, it was noted that the distri-bution of track distances was not the expected uniform one. In Figure 7.17one can clearly see a gap in the middle, an overpopulation at ∼ 1.5 mm,and a uniform distribution inside the cell. The tracks with absolute dis-tances greater than ±7 mm are from bad fits. Many attempts were madeto determine the cause of the apparent missing tracks near the sense wire.Clearly this is not a real physical effect, as the beam spot in our tests is∼ 1 cm × 20 cm wide and could not possibly miss the wire. Somewhere inthe procedure tracks which are close to the wire are being mischaracterized,but we were unable to determine how or why. The Gaussian fits describedabove to determine the resolutions and corrections to be applied were notreliable very close to the wire, because of the low statistics in the histogramsfor tracks close to the wire. This is the origin of the tests of shifting theglobal 0 reference time described in Section 7.2. It was found that shift-ing the global reference by a few nanoseconds increased the population oftracks near the sense wire by a small amount, but not enough to account forthe large gap. The problem is also the origin of the manual enforcement ofthe constraint that signals with 0 ns arrival times should be identified with0 mm distance from the wire. The gap was found early on in the develop-ment of the analysis, and the constraint was added as an attempt to solvethe problem. It did not resolve the issue, but it is a good idea anyways.In order to continue making progress with the project (as I had beenstuck for quite a while at this point), it was decided to ignore the problemand continue the analysis while only considering those tracks that cross the142DOCA (cm)-0.6 -0.4 -0.2 0 0.2 0.4 0.6Resolution (um)100150200250300350400ResolutionDOCA (cm)-0.6 -0.4 -0.2 0 0.2 0.4 0.6Arrival time (us) to Time RelationDOCA (cm)-0.6 -0.4 -0.2 0 0.2 0.4 0.6Correction (cm)-0.0200.020.040.06DOCA CorrectionsFigure 7.16: Plots showing the resolution of the drift chamber (top),time-to-distance relation (middle), and correction to the time-to-distance relation (bottom) at the various levels of iterativeimprovement.143Bad fitsBad fitsGapOverpopulationDistance from wire (mm)Figure 7.17: Distribution of track distances from cell 12, according tothe track fit using the other 7 layers.middle section of the cells between 0.1 and 0.55 cm. This is not as badas it sounds, because generically in drift chambers the resolution becomesmuch worse near the sense wire and near the cell edges. In most cases whenreporting a single value for the resolution of a drift chamber, an average overthe middle part of the cell or the best resolution is used. In Figure 7.16,we ignore the fluctuating resolution curves near the wire at 0 mm, and wenote that the resolution in the middle part of the cell does improve throughthe iterative improvement process. We can finally claim to have measureda resolution of 160µm in the best part of the cell in our prototype usingtraditional tracking means. In comparison, BaBar’s drift chamber has aresolution of 100µm in the best part of its cells.Possible reasons as to why BaBar’s drift chamber had significantly betterresolution than our prototype are as follows: the gas mixture is different,and if the SuperB gas has a higher drift speed, the resolution will suffer;our prototype used mostly off-the-shelf electronics, while BaBar had customelectronics, so our signals may have been noisier; our prototype only used 7layers of cells to determine the “known good” tracks, while BaBar had 40layers, so the contribution to the resolution from the track fitting procedureshould be ∼√40/7 times smaller than with our prototype.1447.6 Timing Clusters7.6.1 MotivationThis thesis and the paper presented in Chapter 4 demonstrates that clus-ter counting improves a drift chamber’s ability to identify particles. Thiswas generally believed even before it was shown to work in drift chambers,since similar techniques were used in time expansion chambers (TECs) sincethe 1970s [62] (a TEC is another type of gaseous ionization detector). Re-searchers are more skeptical of improvements to tracking from cluster count-ing, since no comparable device ever used the technique. Only recently havesome researchers discussed the concept [76, 77]. The work presented in thischapter is the first time that cluster counting has been used for tracking ina full-scale drift chamber under realistic conditions.For particle identification, only the number of clusters is used, as thisis analogous to the traditional measurement of the integrated charge; bothmeasurements are trying to determine the number of primary ionizationevents. In the case of tracking, the number of clusters is not relevant. Theuseful information is the arrival times of the clusters, analogous to the arrivaltime of the whole signal when doing traditional tracking.One could imagine a situation where the number of clusters gives usefultracking information: in long thin cells, the angle of the track would affectthe track length, so the number of clusters (and indeed the integrated charge)would give a measure of the angle. For our prototype and for typical flavour-factory drift chambers, the cells are mostly circularly symmetric, so thenumber of clusters does not reveal information about the track, or at leastno information that we would expect to be an improvement over traditionaltracking.It is clear that cluster counting can help in particle identification: thetraditional method of charge integration requires discarding of data fromthe truncated mean procedure, while the cluster count measurement hasbetter-behaved statistics and allows us to use the information from all layers.For tracking, the reasoning is much less clear. Why should the times of145the clusters beyond the first contain any useful information at all? Afterall, the clusters correspond to primary ionizations, which are independentPoisson-distributed events. The first cluster happens to be the one closestto the point of closest approach, so later clusters should simply give a worsemeasurement of the track distance.The potential improvement can be qualitatively understood by consid-ering two signals in a drift chamber cell such as shown in Figure 7.18. Bothsignals have the same arrival time using the traditional method, but thetimes of the subsequent clusters are very different. The signal at the topof the figure looks suspiciously like a large spurious pulse followed by a realsignal from a charged particle. Such spurious signals can come from con-tamination in the drift chamber (e.g., a charged dust particle accidentallyhitting the wire), from a delta-ray coming from an adjacent cell, or otherkinds of unplanned and difficult-to-account-for sources. The signal at thebottom looks more like a “typical” signal coming from a charged particletrack. Using traditional tracking, these would be effectively identical signals.If we measure the arrival times of the clusters, it will become apparent thatthe top signal is of a different kind than the bottom. A clever algorithm thatdoes not only consider the arrival time of the first pulse edge may effectivelydiscard the first pulse from the top signal, and properly identify the rest ofthe signal as coming from a track far away from the wire.A more mathematical but still qualitative motivation for how clustercounting can help determine a charged particle track is presented in Chap-ter 6. There, a simple theoretical model of a drift chamber cell is constructed,and a Bayesian statistical analysis is done to show how the posterior prob-ability density function for the track impact parameter (distance from thewire) is affected by the information contained in clusters after the first one.7.6.2 Overview of TechniqueFirst an algorithm has to be chosen, and its parameters optimized. This isdescribed in Section 7.6.3. Then all the signals that were previously usedto determine arrival times for traditional tracking are re-analyzed with the146Figure 7.18: Illustration of two signals with the same arrival timeusing the traditional method, but with different arrival timesfor subsequent clusters.cluster-counting algorithm. Using the track distance determined from thetraditional track fitting, we make histograms of the cluster arrival times forsmall intervals of track distance (Figure 7.19). Thus we obtain empiricaldistribution functions for the cluster arrival times as a function of trackdistance from the wire.With these distributions, we now go back to the cluster times in a specificevent and ask the question “from which track distance’s time distribution isthis particular set of times most likely to have been drawn?” To answer this,we calculate the likelihood of drawing that particular set of cluster timesfrom the empirical distribution for each track distance. The likelihood isjust a number proportional to the probability, and the exact calculation isshown in Appendix A.3.The actual quantity calculated is the negative of the log of the likelihood.The logarithm is more convenient numerically because it turns several multi-plications of possibly-tiny numbers into a sum of more reasonable numbers.147Time (ns)200 300 400 500 600 700 80000.0020.0040.0060.0080.010.0120.014Cluster Distribution for distances 0 to 0.0035 cm Entries  2079Mean    403.3RMS     143.5Time (ns)200 300 400 500 600 700 80000.0020.0040.0060.0080.010.0120.0140.0160.0180.020.022Cluster Distribution for distances 0.175 to 0.1785 cm Entries  13039Mean    373.8RMS     143.9Time (ns)200 300 400 500 600 700 80000.0050.010.0150.020.025Cluster Distribution for distances 0.35 to 0.3535 cm Entries  10528Mean    438.5RMS     133.5Time (ns)200 300 400 500 600 700 80000.0020.0040.0060.0080.010.0120.0140.0160.0180.020.022Cluster Distribution for distances 0.525 to 0.5285 cm Entries  10281Mean    519.5RMS     112.2Figure 7.19: Example empirical distribution functions for cluster ar-rival times for four different track distance intervals.The negative is a convention because most computer function-optimizationprograms do minimization, so finding the minimum of the negative log-likelihood is equivalent to finding the maximum of the likelihood itself.With the negative log-likelihoods (NLLs) calculated, it is a simple matterto find the track distance whose NLL is the minimum. That distance isthe cluster-counting equivalent of converting the signal arrival time into adistance using the time-to-distance relation. The equivalent of the resolution- the uncertainty in the time to distance relation - is the shallowness of theminimum in the NLL versus distance graph. The minimum is only searchedfor in part of the cell. Recall that there was an anomalous absence of trackswith distances very-near the sense wire (described at the end of Section 7.5).This made the residuals and resolution measurements difficult, but it alsomars the empirical distribution of cluster times at the extreme edges ofthe cell. As with the residuals and resolutions, our solution for the sake148of making progress is to effectively cut off the ends of the cell, and onlyconsider minima within the finite boundaries 0.1 to 0.55 cm, as anomalousfalse minima sometimes are found outside of these boundaries, simply dueto statistical fluctuations.7.6.3 Algorithms and ParametersThis tracking study was done after the particle identification study describedin Chapter 4. In that study, we found that the specific choice of algorithmwas not so important once the parameters were optimized. Thus for thistracking study, we employ only one algorithm: the “signal above average”described in Section 4.8.2. It was also found that an optimal smoothingtime was ∼ 5 ns, and this was not re-optimized for the tracking study. Theonly parameter that was re-optimized was the threshold, because the optimalthreshold depends on the combined gas and amplifier gain, which is differentin proto 2 than in the single-cell chambers used for the PID study. In thePID study a typical signal amplitude is ∼ 100 mV while for the trackingstudy it is ∼ 1000 mV. Rather than find an appropriate scaling betweenthe two experiments, we simply re-do the optimization of the threshold.With the specific algorithm and smoothing time fixed, the optimization isone-dimensional, so this is a simple task. The optimization is done usinga grid-search method. Several thresholds are tested and evaluated with afigure of merit, and a graph is made to find the optimal value.First we determine the empirical distribution functions for the clustertimes from the data. This is done for each threshold value under consider-ation (Figure 7.20). Then we randomly select a track distance, and retrievethe empirical distribution function for that distance. Simulations using ran-dom numbers are colloquially called “Monte Carlo” in particle physics, evenwhen the technique is relatively simple. Thus we call the randomly-selectedtrack distance the “MC truth” distance.We know the average number of clusters found in a signal at the giventhreshold, so we generate a random cluster count using a Poisson distribu-tion, then randomly draw that number of clusters at times following the149Time (ns)200 300 400 500 600 700 8000.0050.0060.0070.0080.009Threshold 20 mVTime (ns)200 300 400 500 600 700 80000.0050.010.0150.020.0250.03Threshold 55 mVFigure 7.20: A comparison of the empirical distribution functions forthe cluster times at two different thresholds. Both are fortracks between 0.35 and 0.3535 cm from the wire.empirical distribution function at the MC truth distance. These clustertimes are then used to calculate the minimum-NLL track distance, whichwe call the “MC measurement”. In other words, we generate a fake signalgiven the data about a particular track distance, and then ask “how con-sistent is this with the data at that distance?” We do this many times andmake a histogram of the difference between the MC truth and MC measure-ment distances (Figure 7.21). The resulting histograms (one per thresholdtested) contain information about the self-consistency of the cluster infor-mation, i.e., whether the cluster time distributions can actually be used todetermine a track distance. The central value of the histograms gives ameasure of the bias, and the width gives a measure of the uncertainty in adetermined distance.To decide which threshold value is best, we form a figure of merit that150Entries = 10000  Mean   0.01564RMS   0.07179Residuals (Delta cm)0.6− 0.4− 0.2− 0 0.2 0.4 0.6020040060080010001200Figure 7.21: An example residual plot between the “MC truth” trackdistance and the “MC measurement” distance. This is fortracks in the middle part of the cell, using the optimal cluster-counting algorithm parameters (4 ns smoothing, 55 mV thresh-old). The best-fit line is with an asymmetric Laplace distribu-tion.measures the width of the histograms of the MC truth and MC measure-ments. These histograms however are non-Gaussian, so we must be care-ful with the figure of merit. The histograms appear to follow a kind ofasymmetric Laplace distribution. The Laplace distribution is basically twoback-to-back exponential distributions centered at µ:f(x) =12bexp−|x− µ|b(7.4)where µ is the central value and b is the decay constant. In many of ourcases, the decay constants on each side were different, so we fit the following151���������������������������������������������� ��� ��� ��� ��� ��� ��� ��� ��� ���� ������������������������������������Figure 7.22: Full-width at half-maximum of asymmetric Laplace dis-tribution fits to the MC truth-MC measurement residuals atdifferent threshold values. The error bars are derived from theerrors in the fit.function:f(x) =Ab1 + b2exp−x−µb1x >= µexp−µ−xb2 x < µ(7.5)where b1 and b2 are the decay constants on either side of the central value,and A is an overall normalization. The figure of merit chosen is the full-widthat half-maximum of the fitted function, which for the asymmetric Laplacedistribution can be shown to be (b1 + b2) ln 2. Several other figures of meritwere tried: the width of a symmetric Laplace distribution, the inter-quartilerange, and the width parameters of a sum-of-Gaussians. All were consistentwith the one described above. Given our choice, a smaller figure of merit isbetter. In all cases, the central value of the residual plots was much smallerthan the width, indicating zero or negligible bias in the technique.In Figure 7.22 one can see the figure of merit plotted over a large range152of threshold values. Thresholds of 10 to 20 mV have a terrible figure ofmerit, and a plot of the clusters found (Figure 7.23) clearly shows that themeasurement is dominated by fake clusters, because the threshold value iswell-within the noise of the signal. As the threshold is raised out of the noisethe figure of merit improves quite a bit, but then at yet-higher thresholdsit gets worse again. The higher thresholds in the plot are high enough tomiss pulses from real clusters, so that the connection between track distanceand the cluster times becomes less solid. Fortunately the minimum is clearlyvery shallow, so the choice of a threshold of 55 mV is not too critical; as longas we are within ∼ ±10 mV of the minimum the performance is roughly thesame.7.7 Combined LikelihoodIn the particle identification study, the information obtained from clustercounting was combined with the traditional PID from charge integrationvia a combined likelihood. The same thing is done here. The reason isthat clearly any drift chamber built to do cluster counting will also be ableto do the measurements with the traditional techniques. The PID studyshowed that the PID performance was noticeably improved by combiningthe traditional measurement with cluster counting. Here we attempt to dothe same using the cluster times for tracking.The same method will be used here as in the PID study: combinedlikelihood. The negative log likelihood was minimized to find the track dis-tance according to the cluster times (Section 7.6.2), but the traditional mea-surement was only obtained from converting the signal arrival time into adistance (and its uncertainty) using the time-to-distance relation and correc-tions. To convert the traditional measurement into a likelihood, we assumethat the measured distance and uncertainty correspond to the central valueand width of a Gaussian distribution. This is a bad assumption for tracksnear the wire, as mentioned earlier the distribution of signal arrival timesfor tracks near the wire are non-Gaussian and required the use Novosibirskfunctions (Section 7.3). Conveniently, the tracks near the wire have bad1530 200 400 600 800 100020040060080010001200Raw Signal, 47 clusters found TVectorDEntries  1024Mean    497.8RMS     275.70 200 400 600 800 1000200400600800100012004-frame Smoothed Signal (algo0) TVectorDEntries  1024Mean    498.3RMS     275.70 200 400 600 800 1000100−0100200300400500600Thresholded quantity (20 threshold) TVectorDEntries  1024Mean     2550RMS      20270 200 400 600 800 100020040060080010001200Raw Signal, 6 clusters found TVectorDEntries  1024Mean    497.8RMS     275.70 200 400 600 800 1000200400600800100012004-frame Smoothed Signal (algo0) TVectorDEntries  1024Mean    498.3RMS     275.70 200 400 600 800 1000100−0100200300400500600Thresholded quantity (55 threshold) TVectorDEntries  1024Mean     2550RMS      2027Figure 7.23: The same signal analyzed for clusters using two differentthresholds. The three figures on the left use a threshold of20 mV, those on the right 55 mV (the optimal value). Thetriplet of plots features the unprocessed signal, the smoothedsignal, and the actual derived quantity on which the thresholdvalue is applied, at the top, middle, and bottom, respectively.On each plot the identified clusters are indicated with a greencircle. On the derived quantity plot, the threshold is shownwith a dashed red line.statistics and we choose to exclude that part of the cell from our analysis(Section 7.5).The negative log of the Gaussian distribution is quite simple:− lnG(x;µ, σ) = 12(x− µσ)2(7.6)where µ is the central value and σ is the width. Likelihoods for multiple154Distance from wire (cm)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Negative Log Likelihood262728293031323334NLL Using Clusters OnlyMinimum at 0.4305Distance from wire (cm)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Negative Log Likelihood020406080100120140NLL Derived from Traditional TrackingMinimum at 0.408118Distance from wire (cm)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Negative Log Likelihood50100150200250300Combined NLLMinimum at 0.4095Figure 7.24: Plots showing the negative log likelihoods (NLLs) as afunction of track distance computed in three different ways.The top graph shows the NLL using the cluster time informa-tion as described in Section 7.6.2. The middle plot shows thequadratic NLL derived from the traditional tracking distanceand resolution as described in Section 7.7. The bottom plotshows the sum of these two. On each plot is shown two verti-cal lines that delimit the range of searching for the minimum.The location of the minimum on each is shown with an arrow.measurements are multiplied together, so the negative log likelihoods areadded together. This is shown in Figure 7.24 where the negative log Gaus-sian likelihood is shown in the middle plot.The plots in Figure 7.24 show very typical results: the traditional mea-surement yields a certain value and uncertainty, and the corresponding mea-surement using the cluster times yields a mostly-compatible value. This isto be expected, as the arrival time of the first cluster is completely equiva-lent to the arrival time of the whole signal - though they are measured with155Time (ns)200 300 400 500 600 700 80000.0050.010.0150.020.025Distances 0.2975 to 0.301 cm (Fixed Point at 0.3 cm) Entries  5845Mean    422.3RMS     139.1Time (ns)200 300 400 500 600 700 80000.0050.010.0150.020.025Distances 0.392 to 0.3955 cm (Traditional) Entries  4929Mean      458RMS     130.2Time (ns)200 300 400 500 600 700 80000.0050.010.0150.020.025Distances 0.4305 to 0.434 cm (Cluster Info) Entries  5491Mean    477.8RMS     127.9Time (ns)200 300 400 500 600 700 80000.0020.0040.0060.0080.010.0120.0140.0160.0180.020.022Distances 0.497 to 0.5005 cm (Fixed Point at 0.5 cm) Entries  5402Mean    508.3RMS     117.2Figure 7.25: Expected cluster arrival time distributions at four differ-ent distance intervals. The intervals include an arbitrary pointat 0.3 cm, the distance of the track using traditional tracking,the distance of the track using the cluster information in thesignal from cell 12, and another arbitrary point at 0.5 cm. Thearbitrary points are chosen to be much closer and further fromthe wire than either found by the algorithms, respectively. Theactual cluster times are indicated by the arrows. The track andclusters used in the calculation are the same as in Figure 7.24,where a plot of the calculated likelihood values is shown.different algorithms. Indeed from Figure 7.25 one can see that the mostimportant factor in determining the likelihood is whether a cluster (or clus-ters) is found within the peak of the empirical distribution function. Thedifference between the traditional and cluster-based measurements are dueto statistical fluctuations and (hopefully) the additional information con-tained in the later clusters. In the combined likelihood graph, the locationof the minimum is pulled slightly left or right depending on the negative156log likelihood plot of the cluster-based measurement. Typically this pull issmall: rarely do we get very incompatible minima from the two techniques.Furthermore, the variations in the negative log likelihood calculated basedon the traditional method over the width of the cell are ∼ 100, while thevariation in the values from the cluster timing calculation are much smaller.Thus the dominant measurement is still the traditional method, unless aparticularly deep minimum is found with the cluster technique. Indeed theresulting combined-likelihood plot is still mostly parabolic, even after addingthe values from the cluster technique.The location of the minimum in the combined likelihood graph is themeasured value of the track distance with the two methods combined. Thedistances left and right away from the minimum that the graph crossesthe minimum likelihood ±0.5 are used to measure a 1σ uncertainty on thismeasurement.7.8 ResultsTo quantify the contribution of the cluster-time information to the single-cell tracking resolution, we use the same technique as was used to determinethe resolution in the case of traditional tracking. Since the accuracy ofthe track-fitting using 7 layers is much better than the single-cell resolutioneven when only using traditional tracking (40µm compared to 160µm), andwe expect the contribution from cluster-counting to be rather modest, weagain use the 7-layer track fit as a “known good” measurement of the trackposition. We then compare the distance of the track from the wire in cell 12according to the 7-layer track fit with the distance from the wire accordingto the combined-likelihood measurement in cell 12 alone.Histogram of these residuals are made for small intervals of track dis-tance from the wire, and the width of these histograms give the resolution(Figure 7.26). The distributions are very Gaussian-like, so we fit with Gaus-sian functions and use the σ parameter for the resolution. We do this forthe single-cell measurement using just traditional tracking, just the clusterinformation, and with the combined likelihood.157Entries  1299Mean   0.01039RMS    0.04739Cell 12 distance - Track Distance (cm)-0.15 -0.1 -0.05 0 0.05 0.1 0.15020406080100120Track Fitting Residuals (with cluster counting)Figure 7.26: Histogram of residuals between the track distance ac-cording to cell 12 (using the combined likelihood measurement)and the distance accorindg to the track fit using the other 7layers. These are for tracks between 0.259 and 0.2625 cm fromthe wire. Superimposed is the Gaussian fit to the distribution,whose width gives us the resolution in this distance interval.The resulting resolution as a function of track distance can be seen inFigure 7.27. The vertical values are the resolution - the widths of the Gaus-sian fits to the residual histograms, while the error bars are the uncertaintyon that fit parameter. There is no discernable improvement from the addi-tion of cluster counting using this technique.The resolutions using the cluster information only (i.e., without tradi-tional tracking) and using the combined likelihood technique are in factslightly worse than traditional tracking. This may mean that indeed allthe valuable information is in the first cluster, and that the later clustersonly add noise. The additional information from the later clusters is either158Distance (cm)0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5))mµSigma of (Track Distance - Cell Distance (100120140160180200220240260280300Traditional TrackingCluster Counting OnlyCombined LikelihoodFigure 7.27: Single-cell resolution in cell 12 as determined using threetechniques. Note that the bottom of the vertical scale is notat 0µm.not useful, or of such small import that it does not make up for the extravariability from needing to identify the clusters. When averaging over trackdistances, the degradation in resolution between the traditional techniqueand the combined likelihood is ∼ 2.4µm.The technique used to make the cluster-based measurement may alsonot be the only option. One could imagine an algorithm that considers eachcluster one at a time, similar to the Bayesian model presented in Chapter 6.The conclusion is that cluster counting for tracking in proto 2 using thetechnique presented in this chapter is not beneficial. The limitations of theexperiment however do not completely rule out possible benefits in futuredrift chambers, and it may be worthwhile to keep the option open.159Chapter 8Conclusion8.1 Summary of Results8.1.1 GeneralitiesThe two studies presented in this thesis represent the first analyses of datataken from full-length cluster-counting drift chambers. All previous workin the literature has been with small bench-top test chambers. Previoussingle-cell chambers have mostly been so-called “drift tubes” with a singlesense wire in a metal tube. The particle identification study uses a single-cellchamber, but the chamber is constructed using actual field and guard wires.The tracking study uses the first full-length multicell cluster-counting driftchamber ever constructed. Testing realistic detectors is essential, becauseeven if positive results are obtained in smaller or simpler devices, their designmay not necessarily be scalable to large chambers that would actually beused in experiments. For example, a small demonstration chamber can usegeneric coaxial cables (which are quite bulky) for the high-voltage and sensewire connectors, whereas a large drift chamber has to carefully minimize thewire materials.The prototypes used in this work were designed to match the design ofthe eventual SuperB drift chamber. All of these designs were preliminary,as the project was cancelled before a final design as chosen. While each160drift chamber is designed for a particular experiment, the choices made forSuperB should be similar to those made for other flavour-factory or flavourphysics collider experiments. People working on future upgrades to theBelle-II, MEG-II (PSI), or BES-III drift chambers would likely find resultsfrom this thesis to be interesting. Indeed MEG-II is already exploring theoption of using cluster counting for particle identification in their drift cham-ber [77].8.1.2 Particle IdentificationThe most significant result is the measurement of the improved particle iden-tification (PID) when the cluster count is considered alongside the integratedcharge. When requiring 90% of real muons to be rejected (i.e., not identifiedas pions), the efficiency of identifying real pions (i.e., the fraction positivelyidentified) improves from 50% to 60% (Chapter 4). The ionizing behaviourof pions and muons at the momentum of our test beam (210 MeV/c) is al-most the same as for pions and kaons at ∼ 1 GeV/c momentum. This is veryimportant for flavour physics experiments where the typical decay productsof the particles under study are pions and kaons at ∼ 1 GeV/c. Higheridentification efficiency of the daughter particles means that more real com-posite particles (e.g., B-mesons) can be reconstructed for the same amountof data collected. Thus implementing cluster counting for PID can boost theeffective luminosity of the experiment without increasing background rates,or a specific desired signal significance can be obtained with less integratedluminosity.Also very significant is the determination that extremely high-bandwidthelectronics are not needed to acquire a useful signal for cluster counting.Previously it was thought that at a minimum, one would require 1 ns sam-pling times and GHz bandwidths to properly identify clusters. In the PIDstudy our data acquisition system was an oscilloscope taking 0.05 ns samplesand with 4 GHz bandwidth, but the front-end amplifiers had a bandwidth of2.7 GHz. In the process of optimizing the parameters of our cluster-countingalgorithms, it was found that a smoothing time of ∼ 5 ns was optimal. This161means that for a real experiment, the data acquisition system could have asampling rate of only 5 ns, do no smoothing to the waveform, and achievethe same PID improvements as our study. According to the Nyquist sam-pling theorem [78, 79], the minimum bandwidth required to properly recorda signal at a sampling rate of 5 ns is only ∼ 100 MHz. This is very fortunate,because high-bandwidth and high-frequency (∼ GHz) electronics are moreexpensive and consume more power (and thus produce more heat), so ac-commodating them on the endplate of a large drift chamber with thousandsof sense wires would be a difficult engineering challenge. For comparison,the electronics installed in the BaBar drift chamber in 1998 had 200 MHzbandwidth [80].Secondary results of the particle identification study are that the spe-cific choice of algorithm is not so important as long as the parameters areoptimized properly. All algorithms tested gave about the same performanceafter optimization. This means that an analog device such as an application-specific integrated circuit (ASIC) could be used to count the clusters in-stead of a programmable digital device like a field-programmable gate array(FPGA). For the quantity required for a drift chamber, ASICs are morecostly to design and manufacture, but they are much smaller and consumeless power than FPGAs. Considering the time intervals between identifiedclusters did not improve PID performance when used in a tripartite likeli-hood with the cluster count and the integrated charge.8.1.3 TrackingThe main result of the tracking study is that, despite assertions in the lit-erature [76],there is no measurable improvement in the single-cell tracking resolu-tion when cluster information is considered. Our study used a maximum-likelihood technique and empirical cluster time distributions for the cluster-based tracking. The final measurement was done with a combined-likelihoodof both the traditional tracking information and the cluster times. The res-olution of the prototype is 150µm in the best part of the cell, and around162175µm averaged over the middle of the cell. The resolution near the sensewire and near the edge of the cell are not available due to a still-unexplainedgap in the apparent distribution of track distances from the wire.8.2 Future Improvements8.2.1 GeneralitiesMany improvements and corrections to the presented studies are possible.Quite likely if SuperB had not been cancelled, more studies would have beendone, possibly with new prototypes, before the final design and construc-tion of the drift chamber. These studies would have resolved many of theambiguities encountered in the work presented here. New work on cluster-counting drift chambers (such as for MEG-II [77]) will have to address theseissues.In the beam tests for both studies, we had data-taking shifts running24 hours per day in three 8-hour shifts. It was noticeable that the datataken during the graveyard (midnight to morning) shift more frequentlyhad problems than data taken during the other shifts. Problems includedmissing parameters such as temperature and pressure, or hard-to-interpretnotes about anomalies observed. This was particularly apparent for thenight shifts done solo at LNF (the data from which was not analyzed inthis work). For future beam tests I highly recommend going to a four-shift rotation with 6 hour shifts, and always assign shift-takers in pairs at aminimum.In both studies, a lot of data was wasted because anomalies in the datawere discovered only after the beam tests. For example, in the beam test forthe tracking study, it was discovered after data-taking that all the time-of-flight information was somehow uncorrelated with the drift chamber signals.This is likely because of a misconfiguration of the data-acquisition system,and we were unable to correct the problem in the data after the test. Duringdata taking, we had standard sets of histograms and graphs to make aftereach run (so-called “online” analysis), but the process was tedious and not163automated, so the plan was often not adhered to very consistently. More-over, those histograms and graphs would not have identified all problems.In the same example as above, our online analysis made histograms of thetime-of-flight information and the charge integration measurements individ-ually, and these looked normal. We only noticed that the measurementswere uncorrelated on an event-by-event basis when the data was analyzedmore carefully after the mean test (so-called “offline” analysis). As a re-sult, no PID study was possible with the proto 2 data from that beam test.Fortunately it was still possible to perform a tracking study using the self-consistency of the tracks, so the data was not all wasted. More effort indesigning and implementing the online analysis would reduce the wasteddata.8.2.2 Particle IdentificationThe beam tests planned with the single-cell prototypes were quite ambi-tious: we planned to study multiple front-end amplifiers, different cables,wire voltages, and many track positions along the sense wire’s length. Thecombinatoric explosion of permutations meant that not all combinationscould be tested. After data taking, we learned that some large fraction ofthe data was unusable e.g., because of a bad amplifier. So many data runscomparing beam angles and positions were wasted because they were alldone using the same untested amplifier. Future beam tests should be lessambitious about the number of parameters to be tested. If the goal is totest amplifiers, all amplifiers should be tested under essentially the sameconditions (or the same small set of conditions), and compared to a refer-ence amplifier. When possible, redundant data should be taken, becauseoften one learns of a problem with a given data set only after the beam testis done.In the beam test with the single-cell prototypes, the temperature andpressure of the gas in the chamber were not controlled. In the hall wherethe test took place, there is a large door to the outside which was sometimesopened for loading and unloading trucks. There was a large difference in164pressure between the door being opened and closed (∼ 3 mbar). The tem-perature fluctuated with the time of the day and over the course of the weeksof the test. Since the drift chamber operates at the same temperature andpressure as the hall, these parameters were monitored and recorded (crudely,with binoculars and a weather station inside the beam test area). Tempera-ture and pressure can affect the gas gains, so a systematic study of the wirevoltages would have required more consistent (i.e., automatic) recording ofthese parameters. The only significant results from the PID study involvedanalyses of single-run datasets. These data-taking runs were short enoughthat the environmental conditions did not change appreciably during eachrun. Thus to avoid unnecessarily complicating the study, we did not use theactual temperature and pressure information in the analysis.8.2.3 TrackingI was not involved in the construction of the single-cell prototypes for thePID study, but Giuseppe Finocchiaro and I strung every wire in proto 2.There are several things about the construction of proto 2 that could beimproved upon.While stringing the chamber by hand, we first tried wearing latex glovesto avoid touching the wires and feedthroughs with our bare skin. Unfortu-nately the loss of dexterity made it extremely difficult. We soon switchedto manipulating the wire and feedthroughs with bare (but cleaned) handsin order to finish the construction on schedule. Contaminants from contactwith human skin (oils) are mostly a concern for ageing. We only touchedthe outer parts of the feedthroughs, but again there was no clear indicationof what level of cleanliness was required.In the construction of proto 2, we used an epoxy resin to seal gas leaksand smooth over defects in the aluminium structure. This epoxy is thesame that was used for the LHCb straw tubes (Section 5.3), and is presum-ably non-problematic in a drift chamber environment (e.g., no outgassing oforganic molecules), but this was not checked rigorously. Similarly the low-viscosity acrylic used to seal the feedthroughs was not thoroughly checked.165We should have contacted the manufacturers of these adhesives or performedexperiments to determine their suitability for use in a drift chamber.The exact type of acrylic used was actually not written down in an easy-to-find place, which is a serious oversight. We can no longer retroactivelycheck to see if it was an appropriate choice. This was actually a chronicproblem with proto 2, and is likely just a different working style of the Ital-ian collaborators and the TRIUMF group. The Italian collaborators have aPrincipal Investigator, but all team members have equivalent levels of senior-ity or responsibility. While this has clear advantages in terms of flexibilityand collegiality, there is no obvious “boss” to ensure that systematic notesare taken and procedures are laid out and followed. The result is that ifdetailed notes were taken, they are not consistently available to the wholegroup. Were SuperB still an ongoing project, this would not be a problem asthe collaborators would have easy and regular contact with the others. Un-fortunately writing this thesis now nearly three years after the cancellation,many of the details are inaccessible. Indeed a collaborative Wiki that washosted on the INFN website was deleted, and it contained some aggregatednotes that I had transferred there. Having better notes about the electron-ics and data acquisition setup may have allowed us to determine the sourceof the non-correlation between the time-of-flight and the integrated chargemeasurement, and thus perform a PID study with proto 2.The PID study used an external PID device (a time-of-flight detector)which allowed us to use “known good” measurements to compare againstthe drift chamber measurements. For the tracking study, we did not have anexternal tracking system, so the “known good” tracking measurement hadto come from a track fit using 7 out of 8 layers in the prototype. An externaltracker would have allowed us to use all 8 layers and to compare the wholetrack fit to the external tracker’s measurement. We did have an externaltracker ready to use (made of stacked drift tubes), but it stopped functioningshortly before the beam test. With more preparation time, we would havebeen able to arrange an alternate external tracker. Future tracking studiesshould use an external tracker in order to obtain better results.The tracking prototype used terminated sense wires. This means that166a termination resistor (RT in Figure 5.7) was used that minimizes reflectedsignals at the far end of the drift chamber. While this makes the signal anal-ysis more straightforward (one can ignore the possibility of reflected signals),another effect of the resistor is to reduce the total signal amplitude. Evenif the analysis confuses the “true” signal and the reflected one, it is possiblethat better performance is obtained with unterminated sense wires. Thebeam test with the single-cell prototypes in the PID study planned to studythe difference in PID performance between terminated and unterminatedrunning, but due to data-quality issues, we were unable to obtain results.Any future test of a cluster-counting drift chamber should carefully studythe two options to determine which is best.8.2.4 Other IdeasHere are a few ideas and suggestions for improving drift chambers.Nonlinear ADCs and AmplifiersDue to the large statistical fluctuations of drift chamber signal amplitudes,the amplifiers and analog-to-digital converters (ADCs) inevitably encountersaturating signals. For example, if we have an 8-bit ADC whose full scaleis 2 V, any signal above 2 V will register the same as 2 V. The signal is“clipped” at the maximum range of the amplifier or ADC. Thus the large-amplitude signals are badly resolved, and can have bad effects with cluster-counting algorithms that use derivatives. A possible improvement wouldbe to use a non-linear ADC. Most ADCs are linear, and indeed linearityis usually a good property. A linear amplifier is one that maps the digitalvalue to a fraction of the maximum range. For example an 8-bit ADC witha range of voltages from 0 to 2 V would map the digital value 0 to 0 V, thevalue 255 (28 − 1) to 2 V, and intermediate values i to i/255× 2 V.For drift chamber signals, the large-amplitude voltages are more rarethan low amplitude ones, but extremely-large amplitudes still occur. Alinear ADC effectively “wastes” high-order bits on high amplitudes and stillquickly saturates. Another way of saying this is that the ADC has poor167dynamic range. Dynamic range is the ratio of the maximum non-saturatingvoltage that can be measured to the smallest non-zero voltage that can bemeasured. Our example 8-bit amplifier above has a dynamic range of 255:1.ADCs can be built purposely to be non-linear to better match the signalthey are meant to digitize. An example is a logarithmic amplifier, where themapping between the digital value D and the voltage V isV (D) ∝ exp(DNVmaxVmin)(8.1)where Vmax, and Vmin are reference voltages in the ADC and N is the numberof digital values available (255 for an 8-bit ADC). The actual relation willdepend on the design of the amplifier, but dynamic ranges in the thousandsare attainable with 8-bit logarithmic ADCs [81, 82]. Another example of anon-linear ADC is a “dual-range” ADC, which has two linear sections. In adual-range ADC, measurements below or above a given threshold have dif-ferent resolutions. Like the ADCs, nonlinear amplifiers can also be built [83],with the same benefits as nonlinear ADCs.Replacing the Truncated MeanThe truncated-mean procedure is very simple, and was originally used inpart because it was simple to implement with older electronics. It is likelythat a more complex use of the individual charge measurements, withoutdiscarding, can give a robust estimate of the primary ionizations. For ex-ample if the full long-tailed probability distribution was well-measured withknown particle tracks, the later non-truncated measurements could be usedto assigned a likelihood of being a given particle. This was investigated dur-ing the thesis work of fellow SuperB student Rocky So [42], who found thatthe improvement to particle identification performance is modest, comparedto the gains found from cluster counting.168Bibliography[1] J.-F. Caron, et al. Improved particle identification using clustercounting in a full-length drift chamber prototype. Nucl. Instr. Meth.Phys. Res. A, 2014. 735(0):169 – 183. doi:10.1016/j.nima.2013.09.028.→ pages iv, 40[2] B. Gough. GNU Scientific Library Reference Manual - Third Edition.Network Theory Ltd., 3rd edition, 2009. ISBN 0954612078,9780954612078. → pages v, 115, 129[3] R. Brun and F. 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In Material for the First All-Union Conferenceon Questions of Communication, Izd. Red. Upr. Svyazi RKKA,Moscow. 1933 . → pages 162[80] D. Nelson. Babar drift chamber electronics shielding and groundingrequirements. BaBar Note 97-74, 1997. Notes/ → pages 162[81] W. Kester. Intentionally nonlinear ADCs. Tutorial, Analog Devices,2009. Retrieved: July 2015.→ pages 168[82] J. Guo and S. Sonkusale. An area-efficient and low-power logarithmicA/D converter for current-mode sensor array. Sensors Journal, IEEE,2009. 9(12):2042–2043. → pages 168[83] A. J. Peyton and V. Walsh. Analog Electronics with Op-amps: ASource Book of Practical Circuits. Cambridge University Press, 2001.Retrieved: July 2015. → pages 168[84] H. Ikeda, et al. A detailed test of the CsI(Tl) calorimeter for BELLEwith photon beams of energy between 20 MeV and 5.4 GeV. Nucl.Instr. Meth. Phys. Res. A, 2000. 441(3):401 – 426.doi:10.1016/S0168-9002(99)00992-4.→ pages 180178[85] G. Doyle. Singular “they” and the many reasons why it’s correct.Retrieved: July 2015. → pages 185[86] G. Greer. The silver searcher. Retrieved: July 2015. → pages 186[87] E. C. Government of Canada, Department of Justice. Legistics -themself or themselves? Retrieved: July 2015. → pages 186[88] Google. Code of conduct - investor relations. Retrieved: July 2015. → pages186[89] J. Spiro. Defending the Master Race: Conservation, Eugenics, and theLegacy of Madison Grant. University of Vermont Press, 2009. ISBN9781584657156. → pages 189179Appendix ASupporting MaterialsA.1 The Novosibirsk FunctionThe Novosibirsk function was first used to model the energy deposition ina calorimeter by the Belle experiment [84]. Unlike the Belle calorimeterwe have no mathematical derivation from physical principles that motivatesthe use of this particular function. We use it because it is a continuousdeformation of a Gaussian distribution with a semi-infinite range, and itworks well for our purposes (Section 7.3). Figure A.1 shows the normalizedfunction plotted using a few different parameter values.Our Novosibirsk function is defined asF (x;N, xp, σE , η) = N exp(− 12σ20(ln(1 +x− xpσEη))2− σ202)(A.1)where xp is the location of the peak, N is a normalization factor, η is anasymmetry parameter, and σ0 is given byσ0 =2ξsinh−1ηξ2. (A.2)σE is the standard deviation of the Gaussian distribution that is a limitingcase of the Novosibirsk function as η → 0, and ξ is the constant 2√ln 4 ≈2.35 which relates the Gaussian distribution’s standard deviation to the180x0 2 4 6 8 10 12 14ProbabilityDensity00. = 5, σE = 1, η = 1xp = 5, σE = 1, η = 3xp = 5, σE = 3, η = 1xp = 3, σE = 1, η = 1xp = 5, σE = 1, η = 0Figure A.1: Novosibirsk function plotted with various parameters.Each distribution has been normalized to unit area. The tallestcurve has η = 0 and corresponds to a Gaussian. It is tallestbecause it does not have the extended tails from η 6= 0.Novosibirsk function’s full-width at half-maximum. Our function has thex-axis reversed compared to the original reference.Here we show the limiting case of the Novosibirsk function. We will needtwo Taylor expansions for terms in the exponential, one for the logarithmin the numerator, and one for the inverse hyperbolic sine in σ0.ln (1− x) =∞∑n=1(−1)n+1nxn = x− x22+x33− · · · (A.3)sinh−1 x =∞∑n=0(−1)n(2n)!22n(n!)2x2n+12n+ 1= x− 12x33+1 · 32 · 4x55− · · · (A.4)In the context of the limit η → 0, these two series converge absolutely, sowe are free to expand the logarithm and inverse hyperbolic sine inside thesquared bracket to only the leading orders. The argument of the exponential181part of F (x) becomeslimη→0−12((x−xpσEη)− 12(x−xpσE η)2 + h.o)24ξ2(ηξ2 − 16(ηξ2 )3 + h.o.)2 − 2ξ2(ηξ2+ h.o.)2. (A.5)Again, because the series converge absolutely, we can expand the squaredbrackets na¨ıvely, keeping only the leading order terms. The extra termcoming from the lone σ20/2 goes to zero in the limit. The argument of theexponential is nowlimη→0−12(x−xpσEη)2 + h.o.22ξ2(η2ξ24 + h.o.)= −12(x− xpσE)2(A.6)which is immediately recognizable as the argument of the exponential partof a Gaussian distribution with central value xP and standard deviation σE .Thus in the limit η → 0, F (x) becomes a regular Gaussian distribution.The Novosibirsk function also has semi-infinite support as a probabilitydensity function. The limit on x is determined by the logarithmic term. Ifwe require that the logarithm remains real, then1 +x− xpσEη > 0 (A.7)x > xp − σEη. (A.8)As we can see, as η goes to zero, this lower limit goes to −∞ as it shouldfor a Gaussian.A.2 Track Distance From a WireHere we derive D, the absolute distance of the track to a given sense wire,and its uncertainty ∆D. These will be functions of the track parameters (x0and θ), the uncertainty and correlation of the track parameters (∆x0, ∆θ,and cov(θ, x0)), and the sense wire coordinates (xi and yi).182First we define the slope of the track asm =1tan θ(A.9)and the point of closest approach on the track (xp,yp) where:xp = myp + x0 (A.10)andyp = sin2 θ(yi −m(x0 − xi)). (A.11)The actual absolute track distance from the sense wire is thenD(x0, θ) =√(xp − xi)2 + (yp − yi)2 = ||~xp − ~xi||. (A.12)If we focus on the individual squared terms, we will see that D simplifiesa lot.(yp − yi)2 =(sin2 θ(yi − cos θsin θ(x0 − xi))− yi)2(A.13)=((sin2 θ − 1)yi − sin θ cos θ(x0 − xi))2(A.14)=(cos2 θyi + sin θ cos θ(x0 − xi))2(A.15)(xp − xi)2 =(cos θsin θyp + x0 − xi)2(A.16)=(cos θ sin θyi + (cos2 θ − 1)xi + sin θx0)2(A.17)=(cos θ sin θyi + sin2 θ(x0 − xi))2(A.18)Expanding the squared expressions and combining like terms allows sev-eral reductions using sin2 θ + cos2 θ = 1 to finally obtainD = yi cos θ + (x0 − xi) sin θ. (A.19)183Using standard error propagation, we have the uncertainty on D:∆D =[∣∣∣∣∂D∂θ∣∣∣∣2 (∆θ)2 + ∣∣∣∣ ∂D∂x0∣∣∣∣2 (∆x0)2 + 2∂D∂θ ∂D∂x0 cov(θ, x0)] 12(A.20)where cov(θ, x0) is the covariance between θ and x0.Writing out the full expression for ∆D is not so illuminating, as none ofthe terms combine, so it is omitted.A.3 Cluster Time Likelihood CalculationThe empirical distribution function of cluster times at a given track distancefrom the wire is stored in a histogram. The population in each bin of thehistogram represents the average number of clusters expected there usingPoisson statistics. Effectively these are the values µi where i indexes thepossible cluster arrival times. In our case i corresponds to time in nanosec-onds. µi is the expected number of clusters arriving at time i.For a specific signal in a cell, we have a set of real cluster arrival timesxi. i again indexes the time and xi is the number of clusters determinedto have arrived at that time. Practically, xi is always 1, but the code wasmade general enough to accommodate greater multiplicities.The likelihood of having counted xi clusters at time i is a Poisson dis-tribution with mean µi:Li =µxiixi!e−µi . (A.21)For the whole set of clusters, we take the product of the likelihoods of allclusters.In most applications of likelihoods, a more convenient quantity is thenegative of the natural log of the likelihood. This turns the product into asum, and the numerical values are smaller. This simplifies the calculationsand makes numerical computer code more stable.184The final formula for the negative log likelihood isL =∑xi−xi lnµi − µi − ln Γ(xi + 1) (A.22)where the sum is over xi, not i: i.e., we only consider the time bins whereactual clusters were recorded. The log of the factorial is computed usingthe LnGamma function in ROOT for numerical precision. We also have aspecial case where µi = 0, where the first logarithm term would give infinity.µi is only zero when the reference empirical distribution function has zeroexpected clusters at that time. This occurs randomly because some timeshave low statistics, and that bin accidentally has zero clusters in it. Thisis not such a big problem, and the work-around is to virtually expand thesize of the bin. We iteratively sum up the µj of adjacent bins and take theaverage until a nonzero average µi∗ is found. Then this average µi∗ is used inthe formula for the negative log likelihood. Typically only a few bins mustbe averaged before a suitable µi∗ is found.A.4 Superfluous Gendered Language inOpen-Source Project DocumentationSince this project made extensive use of the ROOT framework [3], a largeamount of the documentation was read, and it was noticed that there werefrequent examples where a default-male user was assumed. As an example,in the source file for the TMinuit class, from which the documentation isautomatically generated, one can find this passage (emphasis added):The meaning of the parameters par is of course defined by theuser, who uses the values of those parameters to calculate hisfunction value.There is nothing added by specifying the gender of the user here, and clearlythe original author of the sentence did not mean to specify it. They werelikely using an implied “generic masculine” that is common in many romancelanguages. In English, there is a reasonably well-established tradition ofusing “they” as a gender-neutral singular [85].185I searched through the entire ROOT source code using a tool called TheSilver Searcher [86] for occurrences of the word “he”, “him”, “his”, and“himself”. In some cases, these were legitimate masculines as they werereferences to specific scientists with names like Adam. I made no attemptto discover the actual gender preference of these people, and assumed theirnames were conventional. Other times the “he” was in the phrasing “he orshe” or similar. In these cases I made no changes.In all other cases, I changed the wording to use the gender-neutral“they”, “them”, “their”, and “themself”, and sometimes changed the sen-tence to flow better. “Themself” is more controversial, but it also has anestablished use [87]. Basically “themselves” sounds extra-plural comparedto “they” to me.I purposely did not search for unnecessary specifications of feminine-gendered generic users, because the reality of our society is that the gendersare not treated equally. When reading a manual, seeing a generic masculineis a reflection of our patriarchal state, while seeing a generic feminine is achallenge to it.The various fixes were relatively simple and took little time. The changeswere submitted as a patch by the ROOT developers and current releases nowhave the fix. It turns out that some of the code distributed with ROOT isfrom the “cling” project, so I submitted patches for that part of the codeto the cling where it was accepted. Some of the code in cling is part of apackage for software testing called Google Test. I submitted my patch thereas well, but was met with resistance. Some users were supportive, but themost vocal argued with the “ungrammatical” or “neologistic” wording, orclaimed that the fixed sentences were unreadable. One supporter remindedthe developers of Google Test of this line from the Google Code of Conductfor investors (emphasis added):Failure of a Google contractor, consultant or other covered ser-vice provider to follow the Code can result in termination of theirrelationship with Google. [88]In the end I grew quite uncomfortable with the tone of the discussion on the186Google Test forum, and my changes only affected part of the Google Testcode anyways, so I gave up.If the reader is interested in auditing a piece of open-source software as Idid, the procedure is quite simple. Install The Silver Searcher or the more-commonly-installed “ack” and download the code for the software to beaudited. Navigate to the base directory in your shell, and use the followingcommand:ag − i ”\b ( he | h i s | him | h im s e l f )\b”If you use ack, use “ack” instead of “ag”. The thing in the quotationmarks is a regular expression that will match those whole words, and the-i makes it case-insensitive. The program may find a lot of false positives,e.g., if the code deals with stellar astrophysics (the abbreviation for heliumis He) or if some developers use “his” as variable names for histograms.A.5 Combining Bessel and Struve FunctionsIn Chapter 6 we encountered this form:I0(z)− L0(z) (A.23)where I0 is the modified Bessel function of the first kind at 0th order, andL0 is the modified Struve function at 0th order. Each of the terms has asimple Taylor expansion:I0(z) =∞∑k=0(z2)2k(k!)2, (A.24)andL0(z) =z2∞∑k=0(z2)2k(Γ(k + 3/2))2. (A.25)These expansions look remarkably similar, and indeed it turns out theycan be combined into a single sum. First we recognize that the factorial inEquation A.24 can be written as a Gamma function, and that the sum canbe re-written to be only over even integers.187I0(z) =∞∑n=0,even(z2)nΓ(n/2 + 1)2(A.26)Similarly, Equation A.25 can be rewritten to be a sum over only the oddintegers.L0(z) =∞∑n=1,odd(z2)nΓ(n/2 + 1)2(A.27)The difference of the two functions can then be expressed as a singlealternating sum:I0(z)− L0(z) =∞∑n=0(−1)n ( z2)nΓ(n/2 + 1)2. (A.28)I was unable to find any existing special function which has this Taylorexpansion.A.6 Personal Philosophy of ScienceThe following passages represent my personal philosophy about the purposeof scientific research and its role in society. I am not a scholar of philosophyof science (nor are most scientists), so the arguments therein are not meantto stand up to rigorous philosophical examination. They are here to expressan important part of scientific thought that is often omitted from scientificdiscource: the motivation behind it all.A.6.1 ScienceIn today’s world, science is often a bludgeon used to win arguments andsilence opponents. Many things are called scientific that I would not con-sider as such. Perhaps those who misuse the term simply have a differentdefinition of science, so I should make clear what I mean.Science for me is about seeking truths. We don’t have access to absolutetruths, but science is one of the methods by which we can convince ourselvesthat we are not completely deluded. The kind of truth revealed through sci-ence relies on logical and temporal consistency. While we obviously can’t188claim that the statement “in the presence of massive objects, other mas-sive objects follow certain trajectories” is an absolute truth, it is absolutelyconsistent with all of our experiences and concepts, and we can reasonablyexpect that other people following logical consistency would reach the sameconclusion.Science is a process of refinement. What seems perfectly consistent onone day or in one age might later be revealed to be incorrect or imprecise.A scientific process must always be falsifiable or correctable in some way.Scientists must be fully honest about their claims of truth being based onconsistency alone.There are many kinds of truth and ways of accessing it. Science is onlyone way and it only reveals scientific truths. In many other cases, scienceis completely the wrong approach, or science can only partially inform ar-guments. For example in ethics, policy-making and aesthetics, over-relianceon science to the exclusion of other methods can and has led to terrible deci-sions. For example, in the 19th and early 20th century, then-current scientificknowledge was used to back up decidedly racist and sexist ideologies [89].In our society, scientific knowledge is seen as superior to other kinds ofknowledge, and thus the term “scientific” is often used carelessly as a labelto try to strengthen arguments. Arguments that need such bolstering arerarely of the scientific kind to begin with. Unfortunately most people do notunderstand enough about the philosophy of science to tell the difference, andmisuse of scientific terms makes it very difficult to make good decisions.As a concrete example, consider public reporting about climate change.There is a general consensus in the scientific community that global averagetemperatures are increasing, that the rate of change is increasing, and thatthis change is caused by human industrial activity. It is also generally be-lieved that increased temperatures will lead to more extreme weather, witha negative impact on human well-being from failed agriculture, erosion, andloss of land to the ocean. Unfortunately in public reporting, those tryingto promote this view to the public and those trying to claim that globalwarming is either false or not a problem each call the other non-scientificand try to back up their claims with scientific terminology. To the general189public this can be confusing and creates the appearance of a scientific de-bate when in fact there is a clear general consensus on one side. Most of themost-polluting nations in the world are nominally democratic, so if the pub-lic does not correctly perceive the threat of continued industrial expansionand unsustainable economies, there is little hope for positive change.Another example can be found in the marketing of so-called “alternative”medicine and health products. Terms with well-defined meanings in scienceare abused to sell products. It is possible to find deodorant that claims tocontain “no chemicals” (one must suppose it is made of pure energy, or justelementary particles).Even in otherwise well-meaning groups, science is conflated with otherendeavours that it barely resembles. STEM is an acronym meaning ScienceTechnology Engineering and Mathematics. It is often used when referring torecruitment efforts, e.g., trying to get more women and people of colour toget degrees in these fields. At first glance the term seems like an inoffensivecombination of disciplines, but no one seems to ask why they are groupedtogether. While it’s true that science and engineering both use mathematicalmodels, engineering as a human endeavour is far removed from science as Idefine it above. Lumping the four STEM fields together, given our society’sobsession with immediate results and productivity, erases the possibilitythat science and mathematics could be curiosity-driven, exploratory, andcompletely devoid of marketability. While it’s true that many scientificresults have led to directly useful applications, it is my belief that this shouldnot be the sole motivation for pursuing science as an individual or for fundingscience as a government agency or private funder.A.6.2 Physical SciencePhysical science is applying scientific reasoning to physical systems. Phys-ical systems could be intuitively defined as those which can reasonably beassumed to be universal in nature. As an example, a physical scientific resultis one which we could imagine an unknown alien race on some other planetcoming up with the same result without communicating with us. Physics190such as particles and fields, chemistry of atoms, molecules, and materials,and to some extent, biological systems are all part of physical science.Complex biological systems and social systems I consider to be outsidethe realm of physical science, because they are too unique to our specificsituation on earth. The way animals behave is influenced by the fact thathumans study them, and complex systems can quite reasonably be calledunique. Part of the universality of physical systems is that at some level,each of their members is interchangeable or indistinguishable. As far aswe can tell (and by the laws of quantum mechanics), every electron in theuniverse is actually identical to any other. The same cannot be said formarkets of goods, human psyches, and even animals and plants.This universality is what initially drew me into physics and what con-tinues to fascinate me. I like the fact that the results we get, the truthsthat we claim to access, are independent of political opinions, manipulation,and particular situations. It is important to distinguish the scientific resultsfrom the policy decisions around science. A scientific result could be some-thing about the nature of a particle, but a policy decision would be whetheror not to devote a lot of resources towards doing an experiment. The firstis independent of politics, the second is not.191


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